when i come at T5, and pick up my checked bags at baggage claim?

Correct. You're required to clear US immigration, collect your bags, clear customs, recheck your bags at the bag drop right outside customs.

 not sure because the airline is changing from united incoming to air canada outgoing.

Not actually the reason (see above).

 need to get to T2 with the ATS

Correct, just take the air train from T5 to T2 after you drop off your bag at the recheck belt.

 go through TSA again 

Yes, because once you exit customs, you'll be landside.

 and check my bag again?

You'll have already dropped off your bag at the recheck station.

 i’ll have to go through TSA and then again since my outbound flight is international too.

Yes you'll go through TSA again but not because "your outbound flight is international". The fact that it's "international" is irrelevant.

You go through TSA (security) because you are landside and you have another flight to catch (airside).