70 amp breaker what size wire do you run for equipment that is 50' away and pulls 55 amps?

What equipment? #4 THHN/THWN

It depends on the equipment. Either #6cu or #4cu, but most likely #4.

#6 may likely work(don't know what equipment), No matter what, 4 would decrease voltage drop, and like Stan says #6 is likely code and acceptable.
Whenever you are undecided, larger is better, you can adjust breaker size.
The price difference of the wire is minimal compared to the labor involved.