I think it was arbitrary, as a way to get people to buy more at the time. At any rate, the limit of 5 is vestigial limit reminiscent of an older Idle era before superpowers existed

and what about the useless "skip level"?

Skip level is by far the most useful power lol. The here skip level strat is op.
Levels will be unlocked again after you ascend or super-ascend. Skip level power makes your runs much quicker by skipping over bad levels or by using the here skip level strat.

why the powers are limited to 5 ?

Actually you can have more than 5 powers of each kind. After reaching 5, you cannot collect from the map or from daily bonus, but you can still collect powers from other ways. For example from the wheel, from paying in special events, from battle rewards, from clan rewards, etc

Dear Mathematician,

i was just talking about the "skip level" power...
by now I have 5 skip level powers. there are 2 on the map i am playing, but i will never get them as i have already unlocked all powers, so they are just lost, and of no use. And i will never collect them or any in the next maps after europe Huge!!
that was what i was saying, maybe not so clearly i apologise

Mathematician’s point is the single furthest/best idle player uses superpower skip level to achieve it.

I have understood but who will give an answer to my question...:
What do to with skip levels when all maps are unlocked any you got 5 in stocks, and you get again several ones in the next maps...?

When you ascend, but more importantly when you super ascend, they lock again. Here uses super ascension to superpower, unlock everthing, run it for a day, and abandon for AP, then go back and finish it.

What do to with skip levels when all maps are unlocked

Levels are locked again when you ascend or super-ascend.

so they are just lost, and of no use. And I will never collect them

No. The powers are still on the map if you haven't collected them. You can still collect them if you play the map again in the future, probably after you ascended or super-ascended.

The problem is idle is programmed to be tolerant of offline play but expects the same instance to be active when the internet connection resumes. Additionally, the client does not sync with the server very often. I had loads of problems with this early on but now I manually sync each time I stop playing CTRL ALT G

This should not be necessary; little would be lost by having the game only playable in online only mode; I can only imagine it's to reduce server load. It seems to be programmed in a way that your save game file is generated on your local browser and after a few checks is uploaded to a sql database. I don't know what the auto save interval is but it's rather large.

the interval is 10 minutes, and the reason for it not being quicker is because cost, Fizzer told me this.