Billing Cycle question

We have a calendar period of 4-4-5.

Our billing happens at the end of the period (not month) e.g. this month the period end is 25th May, then that is the date that becomes the billing cycle date.

I don't see any such option in Billing Cycle setup. I only see end of the month. What options we have here.

Also note there are few projects which bills middle of the month (15th every time). Please let me know how both of these requirements run in conjunction