diff --git a/swh/objstorage/replayer/replay.py b/swh/objstorage/replayer/replay.py
index f22d550..f4e1b9b 100644
--- a/swh/objstorage/replayer/replay.py
+++ b/swh/objstorage/replayer/replay.py
@@ -1,298 +1,307 @@
 # Copyright (C) 2019-2020 The Software Heritage developers
 # See the AUTHORS file at the top-level directory of this distribution
 # License: GNU General Public License version 3, or any later version
 # See top-level LICENSE file for more information
 
 import logging
 from time import time
 from typing import Callable, Dict, List, Optional
 
 from sentry_sdk import capture_exception, push_scope
 
 try:
     from systemd.daemon import notify
 except ImportError:
     notify = None
 
 from tenacity import (
     retry,
     retry_if_exception_type,
     stop_after_attempt,
     wait_random_exponential,
 )
 
 from swh.core.statsd import statsd
 from swh.model.hashutil import hash_to_hex
 from swh.model.model import SHA1_SIZE
 from swh.objstorage.objstorage import ID_HASH_ALGO, ObjNotFoundError, ObjStorage
 
 logger = logging.getLogger(__name__)
 
 CONTENT_OPERATIONS_METRIC = "swh_content_replayer_operations_total"
 CONTENT_RETRY_METRIC = "swh_content_replayer_retries_total"
 CONTENT_BYTES_METRIC = "swh_content_replayer_bytes"
 CONTENT_DURATION_METRIC = "swh_content_replayer_duration_seconds"
 
 
 def is_hash_in_bytearray(hash_, array, nb_hashes, hash_size=SHA1_SIZE):
     """
     Checks if the given hash is in the provided `array`. The array must be
     a *sorted* list of sha1 hashes, and contain `nb_hashes` hashes
     (so its size must by `nb_hashes*hash_size` bytes).
 
     Args:
         hash_ (bytes): the hash to look for
         array (bytes): a sorted concatenated array of hashes (may be of
             any type supporting slice indexing, eg. :class:`mmap.mmap`)
         nb_hashes (int): number of hashes in the array
         hash_size (int): size of a hash (defaults to 20, for SHA1)
 
     Example:
 
     >>> import os
     >>> hash1 = os.urandom(20)
     >>> hash2 = os.urandom(20)
     >>> hash3 = os.urandom(20)
     >>> array = b''.join(sorted([hash1, hash2]))
     >>> is_hash_in_bytearray(hash1, array, 2)
     True
     >>> is_hash_in_bytearray(hash2, array, 2)
     True
     >>> is_hash_in_bytearray(hash3, array, 2)
     False
     """
     if len(hash_) != hash_size:
         raise ValueError("hash_ does not match the provided hash_size.")
 
     def get_hash(position):
         return array[position * hash_size : (position + 1) * hash_size]
 
     # Regular dichotomy:
     left = 0
     right = nb_hashes
     while left < right - 1:
         middle = int((right + left) / 2)
         pivot = get_hash(middle)
         if pivot == hash_:
             return True
         elif pivot < hash_:
             left = middle
         else:
             right = middle
     return get_hash(left) == hash_
 
 
 class ReplayError(Exception):
     """An error occurred during the replay of an object"""
 
     def __init__(self, operation, *, obj_id, exc):
         self.operation = operation
         self.obj_id = hash_to_hex(obj_id)
         self.exc = exc
 
     def __str__(self):
         return "ReplayError(doing %s, %s, %s)" % (self.operation, self.obj_id, self.exc)
 
 
-def log_replay_retry(retry_obj, sleep, last_result):
+def log_replay_retry(retry_state, sleep=None, last_result=None):
     """Log a retry of the content replayer"""
-    exc = last_result.exception()
+    try:
+        exc = retry_state.outcome.exception()
+        attempt_number = retry_state.attempt_number
+    except AttributeError:
+        # tenacity < 5.0
+        exc = last_result.exception()
+        attempt_number = retry_state.statistics["attempt_number"]
+
     logger.debug(
         "Retry operation %(operation)s on %(obj_id)s: %(exc)s",
         {"operation": exc.operation, "obj_id": exc.obj_id, "exc": str(exc.exc)},
     )
 
     statsd.increment(
         CONTENT_RETRY_METRIC,
-        tags={
-            "operation": exc.operation,
-            "attempt": str(retry_obj.statistics["attempt_number"]),
-        },
+        tags={"operation": exc.operation, "attempt": str(attempt_number),},
     )
 
 
-def log_replay_error(last_attempt):
+def log_replay_error(retry_state):
     """Log a replay error to sentry"""
-    exc = last_attempt.exception()
+    try:
+        exc = retry_state.outcome.exception()
+    except AttributeError:
+        # tenacity < 5.0
+        exc = retry_state.exception()
+
     with push_scope() as scope:
         scope.set_tag("operation", exc.operation)
         scope.set_extra("obj_id", exc.obj_id)
         capture_exception(exc.exc)
 
     logger.error(
         "Failed operation %(operation)s on %(obj_id)s after %(retries)s"
         " retries: %(exc)s",
         {
             "obj_id": exc.obj_id,
             "operation": exc.operation,
             "exc": str(exc.exc),
-            "retries": last_attempt.attempt_number,
+            "retries": retry_state.attempt_number,
         },
     )
 
     return None
 
 
 CONTENT_REPLAY_RETRIES = 3
 
 content_replay_retry = retry(
     retry=retry_if_exception_type(ReplayError),
     stop=stop_after_attempt(CONTENT_REPLAY_RETRIES),
     wait=wait_random_exponential(multiplier=1, max=60),
     before_sleep=log_replay_retry,
     retry_error_callback=log_replay_error,
 )
 
 
 @content_replay_retry
 def copy_object(obj_id, src, dst):
     hex_obj_id = hash_to_hex(obj_id)
     obj = ""
     try:
         with statsd.timed(CONTENT_DURATION_METRIC, tags={"request": "get"}):
             obj = src.get(obj_id)
             logger.debug("retrieved %(obj_id)s", {"obj_id": hex_obj_id})
 
         with statsd.timed(CONTENT_DURATION_METRIC, tags={"request": "put"}):
             dst.add(obj, obj_id=obj_id, check_presence=False)
             logger.debug("copied %(obj_id)s", {"obj_id": hex_obj_id})
         statsd.increment(CONTENT_BYTES_METRIC, len(obj))
     except ObjNotFoundError:
         logger.error(
             "Failed to copy %(obj_id)s: object not found", {"obj_id": hex_obj_id}
         )
         raise
     except Exception as exc:
         raise ReplayError("copy", obj_id=obj_id, exc=exc) from None
     return len(obj)
 
 
 @content_replay_retry
 def obj_in_objstorage(obj_id, dst):
     """Check if an object is already in an objstorage, tenaciously"""
     try:
         return obj_id in dst
     except Exception as exc:
         raise ReplayError("in_dst", obj_id=obj_id, exc=exc) from None
 
 
 def process_replay_objects_content(
     all_objects: Dict[str, List[dict]],
     *,
     src: ObjStorage,
     dst: ObjStorage,
     exclude_fn: Optional[Callable[[dict], bool]] = None,
     check_dst: bool = True,
 ):
     """
     Takes a list of records from Kafka (see
     :py:func:`swh.journal.client.JournalClient.process`) and copies them
     from the `src` objstorage to the `dst` objstorage, if:
 
     * `obj['status']` is `'visible'`
     * `exclude_fn(obj)` is `False` (if `exclude_fn` is provided)
     * `obj['sha1'] not in dst` (if `check_dst` is True)
 
     Args:
         all_objects: Objects passed by the Kafka client. Most importantly,
             `all_objects['content'][*]['sha1']` is the sha1 hash of each
             content.
         src: An object storage (see :py:func:`swh.objstorage.get_objstorage`)
         dst: An object storage (see :py:func:`swh.objstorage.get_objstorage`)
         exclude_fn: Determines whether an object should be copied.
         check_dst: Determines whether we should check the destination
             objstorage before copying.
 
     Example:
 
     >>> from swh.objstorage.factory import get_objstorage
     >>> src = get_objstorage('memory')
     >>> dst = get_objstorage('memory')
     >>> id1 = src.add(b'foo bar')
     >>> id2 = src.add(b'baz qux')
     >>> kafka_partitions = {
     ...     'content': [
     ...         {
     ...             'sha1': id1,
     ...             'status': 'visible',
     ...         },
     ...         {
     ...             'sha1': id2,
     ...             'status': 'visible',
     ...         },
     ...     ]
     ... }
     >>> process_replay_objects_content(
     ...     kafka_partitions, src=src, dst=dst,
     ...     exclude_fn=lambda obj: obj['sha1'] == id1)
     >>> id1 in dst
     False
     >>> id2 in dst
     True
     """
     vol = []
     nb_skipped = 0
     nb_failures = 0
     t0 = time()
 
     for (object_type, objects) in all_objects.items():
         if object_type != "content":
             logger.warning(
                 "Received a series of %s, this should not happen", object_type
             )
             continue
         for obj in objects:
             obj_id = obj[ID_HASH_ALGO]
             if obj["status"] != "visible":
                 nb_skipped += 1
                 logger.debug(
                     "skipped %s (status=%s)", hash_to_hex(obj_id), obj["status"]
                 )
                 statsd.increment(
                     CONTENT_OPERATIONS_METRIC,
                     tags={"decision": "skipped", "status": obj["status"]},
                 )
             elif exclude_fn and exclude_fn(obj):
                 nb_skipped += 1
                 logger.debug("skipped %s (manually excluded)", hash_to_hex(obj_id))
                 statsd.increment(
                     CONTENT_OPERATIONS_METRIC, tags={"decision": "excluded"}
                 )
             elif check_dst and obj_in_objstorage(obj_id, dst):
                 nb_skipped += 1
                 logger.debug("skipped %s (in dst)", hash_to_hex(obj_id))
                 statsd.increment(CONTENT_OPERATIONS_METRIC, tags={"decision": "in_dst"})
             else:
                 try:
                     copied = copy_object(obj_id, src, dst)
                 except ObjNotFoundError:
                     nb_skipped += 1
                     statsd.increment(
                         CONTENT_OPERATIONS_METRIC, tags={"decision": "not_in_src"}
                     )
                 else:
                     if copied is None:
                         nb_failures += 1
                         statsd.increment(
                             CONTENT_OPERATIONS_METRIC, tags={"decision": "failed"}
                         )
                     else:
                         vol.append(copied)
                         statsd.increment(
                             CONTENT_OPERATIONS_METRIC, tags={"decision": "copied"}
                         )
 
     dt = time() - t0
     logger.info(
         "processed %s content objects in %.1fsec "
         "(%.1f obj/sec, %.1fMB/sec) - %d failed - %d skipped",
         len(vol),
         dt,
         len(vol) / dt,
         sum(vol) / 1024 / 1024 / dt,
         nb_failures,
         nb_skipped,
     )
 
     if notify:
         notify("WATCHDOG=1")