SB push with 53s ... stay with me

[locutus2002]

Villain has 4XBB left as stated in the problem, the BB is a sunk cost. Villain gets 5XBB:4XBB pot odds and has to be 44% in the hand against hero's range to make the call. Less if you are willing to take an EV- proposition on a micro stack.

What is hero's range for pushing? Judging from the donktastic responses it's any two.

From my point of view your logic is flawed, the more chips villain has the wider range hero should push. However 53s should not be in any pushing range where you can resonably expect villain to call.