When charging an entrance in Zoomaka do I give change?
No.

I presume from the title you've played the relevant Entrance card to charge the fee.

From the rules, page 10:


  When paying a debt no change is returned.


The player could choose to pay with assets from their zoo instead of using the full 5-cost banked card, though this might make more sense if the total cost were, for example, 7.