There was indeed a Windows 3.11 and the much more common Windows for Workgroups 3.11 which was a profoundly different product (32-bit disk subsystem & 32-bit networking subsystem -- the first time these pillars of Win9x went out into the world.)

But neither of them ran on any particular version of DOS. They ran on PC DOS, MS-DOS and DR-DOS -- although Microsoft tried very hard to block the latter:

https://en.wikipedia.org/wiki/AARD_code

They ran on DOS 3.3, 4, 5, 6, and 7.

There's nothing at all that links them especially to MS-DOS 5.