I was under the impression that somebody said the max # of a powers you could get was 5 - if you got more, you were forced to used one..

However, I currently have 6/5 on a particular power...

you can only pick up 5/5 powers in idle (either from the map, or from the daily bonus).

this does not apply to gifts (from: raffles, the wheel, forum threads, Fizzer himself), so they can stack over the limit of 5

BUT... all the power ups you claim on a map can't be added to your inventory until you make space for it, or you can use it directly on that level.

Same goes for power ups from daily rewards.

Related topic that we need an answer for but don't have one yet:
https://www.warzone.com/Forum/445178-power-ups-maps-wasted-remain