I see joining Idle premium gives you a one time shot at 5x of every power up.

If I'm already sitting on some, will I lose those and/or be forced to use them right away? Does the cap increase?

I was stocking up to hit some of the harderned levels, but dont want to loose out on a big one time power spike because I was being "frugal" with my abilities.

Your power counts can go above five when you get them from most sources.

I currently have 459 Supercharge Mine powers, for example.

The two exceptions that I am aware of:

1. you won't pick up powers from the ground if you are at or above five.
2. the daily door prizes must be used or discarded if you are at or above five.

Powers from other sources (wheel, battles, clan wars, etc) stack above five.

I haven't received any powers from purchases, but I assume they do as well.

Presumably someone will come along and confirm this.

You can drag the daily door prize away though, don't hit claim if you're full at 5, just move the window to the corner or backout, they'll keep adding up

Back out of what? The level? I just opened the door to find a Supercharge Army Camp, backed out of the level, and when I re-opened it, I had the same number of SAC powers as I did before.

What really?! now I wanna try it on my door prize tomorrow, but yeah I thought they kept on stacking up

You can click the door to reveal your prize and drag that window away until you're ready to claim it, I've done this many times, with the caveat that if you refresh (or similar) it will be lost to the great bit bucket in the sky. I will say I haven't ever left it the ~20h necessary to see if another one will pop up before claiming it though.

If you dont claim the door and leave, or lose the window it wont be added to your power pool