tl;dr: Euros are being given, not received.
Here’s the first definiton of exchange in the American Heritage Dictionary:
exchange v.tr.
1. To give in return for something received; trade: exchange dollars for francs; exchanging labor for room and board.
Source: American Heritage Dictionary of the English Language
via The Free
Dictionary
Let’s use that to investigate your issue:
Question Passive: How many euros can [be given in return] for 5 USD?
Answer Passive: 4.57 euros can [be given in return] for 5 USD.
Question Active: How many euros can I/you/the bank [give in return] for 5 USD?
Answer Active: You/I/the bank can [give] 4.57 euros [in return] for 5 USD.
To test—if you must—swap in a cat for the five bucks:
Question Passive: How many euros can [be given in return] for this cat?
Answer Passive: 4.57 euros can [be given in return] for this cat.
Question Active: How many euros can I/you/the pet store [give in return] for this cat?
Answer Active: You/I/the pet store can [give] 4.57 euros [in return] for this cat.