You should have no problems with that combination as long as you don't try to play it very loud, which you are not going to do.

The receiver is rated for 70 watts per channel with two channels driven, for a total power of 140 watts.

Dividing that up between five channels gives only 28 watts per channel, so that will definitely force you to keep the peak volumes modest to avoid distortion, but it's probably adequate if a bit of restraint is used.

The Jamo speakers are rated at 6 ohm and the audioengine at 8 ohm. The receiver has instructions specific to using speakers that are rated less than 6 ohm and I would read that section and implement the Jamos as if they were less than 6 ohm if the receiver trips its thermal protection device and shuts down.

Give the receiver plenty of space above it to breathe and stay cool and you should be fine. Don't stack anything on top or enclose it in a cabinet that can't circulate air if it shuts down while in use as that would indicate that it's running too hot.

I'd trust the Audioengine specs over the other link and so it would present a potential problem. If I already had the gear I wouldn't hesitate to give it a go. If I was looking at purchasing the gear, I'd reconsider and play it safe unless I had other future intentions for the P4 speakers specifically.

Receivers can take a little abuse and employ their thermal protection without damage, but you'll have to decide for youself whether you want to take the chance of having to replace the P4s with something else if your amp continually overheats. Surround speakers aren't that critical in your situation and I'd look for amp friendly speakers given the electronics being used.