Please see what's marked for download in the Admin View of Update Manager (Configuration -> Patch Download Sources).
Don't the patches show up in the Repository when you enter 5.1 in the search box?
From the screenshots it looks like the configuration is ok. The download location for version 4 and 5 patches is the same (that's why you cannot download just v5 patches). The patches for ESXi 5 should actually show up as "embeddedESX 5.x"!?