Can I install a 50A breaker in a 70A sub-panel with other breakers installed?
There is not enough information to give a yes or no answer. The breaker that supplies this panel and the wire size would be needed to say if it would work. Can a 50 amp breaker be installed in a 70 amp panel yes. Can this be done if the total of all the breakers add up to more than the panel rating? Yes but the over current protective device (breaker) feeding the panel can not be more than 70 amps. One easy example would be for a heating and cooling sub panel lets say 60a of electric heat and a 30a AC unit total 90 amps but it is legal because only 1 load would be used at a time. So in short a 50 amp breaker can be used in a 70 amp panel but if your breaker feeding the panel or the wiring is not sufficient size it won't work.