diff --git a/Lib/mailbox.py b/Lib/mailbox.py
index 73c43e2..8b00460 100644
--- a/Lib/mailbox.py
+++ b/Lib/mailbox.py
@@ -691,6 +691,9 @@
         _sync_close(new_file)
         # self._file is about to get replaced, so no need to sync.
         self._file.close()
+        # Make sure the new file's mode is the same as the old file's
+        mode = os.stat(self._path).st_mode
+        os.chmod(new_file.name, mode)
         try:
             os.rename(new_file.name, self._path)
         except OSError as e:
diff --git a/Lib/test/test_mailbox.py b/Lib/test/test_mailbox.py
index d8dca1d..9f1fdad 100644
--- a/Lib/test/test_mailbox.py
+++ b/Lib/test/test_mailbox.py
@@ -966,6 +966,23 @@
         self._box = self._factory(self._path)
         self.assertEqual(len(self._box), 1)
 
+    def test_permissions_after_flush(self):
+        # See issue #5346
+
+        # Make the mailbox world writable. It's unlikely that the new
+        # mailbox file would have these permissions after flush(),
+        # because umask usually prevents it.
+        mode = os.stat(self._path).st_mode | 0o666
+        os.chmod(self._path, mode)
+
+        self._box.add(self._template % 0)
+        i = self._box.add(self._template % 1)
+        # Need to remove one message to make flush() create a new file
+        self._box.remove(i)
+        self._box.flush()
+
+        self.assertEqual(os.stat(self._path).st_mode, mode)
+
 
 class _TestMboxMMDF(_TestSingleFile):