You get 20 normal and 5 friend attempts a week.

You can do 5 normal a day and friend anytime.

So after 4 days, you could run out, so it will be 0 until Monday.

20 normal per week not 5 attempts per day?

It's BOTH.

i.e. you can't do more than 5 per day and you can't do more than 20 per week.

So basically if I do 5 attempts every day for 4 days (Mon,Tue,Wed and Thur), I will have 0 attempts left for the rest of the week?

If you do it with friends who have a friendship level of over 5 (I believe), you will have 5 additional attempts that are not factored into the '5 per day limit' in the same week (meaning you can do up to 10 (5 + 5) on Monday, if you'd like). This totals to 25 attempts per week (20 + 5). To reply to your statement, yes, that is essentially correct. I believe it does consume your friendship attempts first though, so if you only do 5 on Monday with your friends, you still have the 20 weekly attempt left, with 0 friendship attempt for the rest of the week.