diff --git a/setup.py b/setup.py
index 81b64e527..feb7f5c33 100644
--- a/setup.py
+++ b/setup.py
@@ -67,10 +67,10 @@
 install_requires = [
     # we are rather picky about msgpack versions, because a good working msgpack is
     # very important for borg, see: https://github.com/borgbackup/borg/issues/3753
-    'msgpack >=0.5.6, <=1.0.4, !=1.0.1',
     # Please note:
-    # using any other version is not supported by borg development and
+    # using any other msgpack version is not supported by borg development and
     # any feedback related to issues caused by this will be ignored.
+    'msgpack >=0.5.6, <=1.0.5, !=1.0.1',
     'packaging',
 ]
 
diff --git a/src/borg/helpers/msgpack.py b/src/borg/helpers/msgpack.py
index 3c98b1358..3c6565639 100644
--- a/src/borg/helpers/msgpack.py
+++ b/src/borg/helpers/msgpack.py
@@ -182,7 +182,7 @@ def is_slow_msgpack():
 def is_supported_msgpack():
     # DO NOT CHANGE OR REMOVE! See also requirements and comments in setup.py.
     import msgpack
-    return (0, 5, 6) <= msgpack.version <= (1, 0, 4) and \
+    return (0, 5, 6) <= msgpack.version <= (1, 0, 5) and \
            msgpack.version not in [(1, 0, 1), ]  # < add bad releases here to deny list