Time will vary greatly.

The walk from your gate will be about 10 minutes if you land at the far end of T5.

The wait for immigration will be 10-15 minutes (maybe more) if you are US citizen. Probably longer if not. Try to choose your line by the looks of the people in it, not by the length. Choose the line with lots of couples who were clearly on vacation, etc., and it will most likely move fast. A bunch of business people is also good. I'm usually flying business, and I tend to arrive at immigration with mostly seasoned travellers so the line tends to move quickly at that point.

The wait for baggage can take forever. One reason I don't check bags for INTL travel.

The line for customs always moves very quickly. Even when we were sent for secondary instpection (cat food, don't ask) it was no more than 5 extra minutes.

When you're through customs you're out the doors and done.

Best case:

plane door to immigration - 5 minutes
immigration - 10 minutes
baggage - 0
customs - 0
TOTAL 15 minutes

Worst case:

plane door to immigration - 10 minutes
immigration - 20 minutes (US) 30 minutes (non-US)
baggage - 30 minutes (the longer you stay in immigration the less time you'll wait for your bags, so these two things tend to even out in the end. I've always gotten through immigration before my bags were out, making the effective immigration wait zero)
customs - 5 minutes
TOTAL 65 minutes (US) 75 minutes (non-US)

I don't think the process has ever taken me more than 40 minutes with baggage. And, I have indeed done it in 15 or less.

If changing to a domestic flight, to this you will need to add the time rechecking bags - 10 minutes? (I've never done it). Walking to the little train - 10 minutes. Taking the train to T1 or T2 - 10 minutes (max waiting time for train midday 4-5 minutes, the trip 5 minutes).

You then need to get from the train to the gate - 5 to 20 minutes or more. Assuming you already have your BP (either from the original checkin or when you rechecked your bags) you will need to walk from the train to security - 5 minutes, wait for security - 5 minutes to 20 minutes, and walk to your gate - 5 minutes to 20 minutes depending on gate location.