diff --git a/synapseclient/client.py b/synapseclient/client.py
index 61bcf73c5..cbc94c2f1 100644
--- a/synapseclient/client.py
+++ b/synapseclient/client.py
@@ -335,7 +335,7 @@ def __init__(
 
         httpx_timeout = httpx.Timeout(70, pool=None)
         self._requests_session_storage = requests_session_storage or httpx.Client(
-            timeout=httpx_timeout
+            limits=httpx.Limits(max_connections=5), timeout=httpx_timeout
         )
 
         cache_root_dir = (
@@ -427,7 +427,7 @@ async def close_connection() -> None:
         self._requests_session_async_synapse.update(
             {
                 asyncio_event_loop: httpx.AsyncClient(
-                    limits=httpx.Limits(max_connections=25),
+                    limits=httpx.Limits(max_connections=5),
                     timeout=httpx_timeout,
                 )
             }