And if a player prolongs the game for several months, then it's a different balance altogether. Let them choose a build and not take Chaos. You can't and shouldn't balance everything for all possible game lengths.
I would discard such a perk. Once or twice during the game, you get a couple of peasants, and that's it. The point is, if perks aren't desirable, then what's the point of having them?
A week is a plus one increase of levels 1-3, and for them, another +10% per week. I won't count levels 4 and higher for simplicity (I'll compensate by considering the increases of levels 1-3 to be at their maximum right away).
So, the second week is two increases + 10% of the first = 210%.
The third week is 2.1 * 1.1 + 1 = 3.31.
The fourth week is 4.64.
The fifth week is 6.1.
The sixth week is 7.71.
The seventh week is 10.58.
The eighth, final week is 12.64.
So, in the end, the increase has grown... by a factor of 1.5 for levels 1-3. Yes, there are many assumptions in the calculation, but the pros and cons more or less compensate for each other. Now let's look at your 5% per day:
In a week, 5% will give 40%. Well, let's say 30 due to rounding down. Let's calculate.
The second week is 1.3 + 1 = 2.3.
The third week is 4.
The fourth week is 6.2.
The fifth week is 9.06.
The sixth week is 12.77.
The seventh week is 17.6.
The eighth week is almost 24! Three times as much, Karl! Roughly speaking, if you delay for some reason for a week, the situation goes from unpleasant to hopeless. And if the opponent is playing as Necropolis... Hmm.