If a pawn was in the safety zone, does the player have to pick up the card with the exact number of spaces to get Home? For example if the pawn was 5 spaces from Home, would the player have to get a 5 card, or could they draw a 3 and then a 2?
You can enter the safe zone, sure. And you can move forward in there even if you don't make it all the way to the home space. So if you're five spaces from Home, you could cover that distance with a 3 and then a 2, yes.
You need exact count to enter the home space.
The rules are explicit on this:
Rules (emphasis added):
Only you may enter your own color safety zone. All other rules apply.
You must bring all three of your pawns into home by exact count.