how will having a free period affect my college apps?

i will be a senior next year and i am planning to take 5 aps along with classes at a local community college. i have probably the most rigorous schedule out of all the juniors right now and i am running out of classes that suit my interests.

would taking a free period next year negatively affect my app? would being a TA be better?

https://www.collegeconfidential.com/search-results?q=%22free%20period%22

No.
You have a full schedule at the highest possible rigor - no need to add fluff. Take the free period.

Use some of that time to research targets, what they consider a valid range of rigor.

even my Freshman have open periods b/c our school cannot afford to hire enough teachers to fill up schedules. (Total of 5 open periods for my 3 kids this year-- Junior plans to fill 2/3 with TA periods). I am confident that the rigor of their remaining courses will compensate. We’re on a trimester system; APs offered only Tri 1-2 so all AP students have very light loads Trimester 3. Colleges hopefully dig deep than allocating a penalty for an open period.

for reference, this year i am taking ap calc bc, ap stats, ap lang, ap physics c, ap seminar, apush (online), and mandarin 3

next year i plan to take ap research, ap lit, ap art history, ap econ, ap chinese, and possibly some advance math at a community college.

also, my school runs on 6 periods a day

Most seniors at my kids’ top public school have a free period senior year and many get into highly selective colleges. It’s considered normal.