whats the expected value of getting a 5 dollar bill as a gift?

You need the probability and then you can compute the expected value.

For example, let's say that 20% of the time you get $5. But 80% of the time you get $0.

E(X) = (0.2 * 5) + (0.8 * 0)

= 1 + 0

= 1

So your expected value is $1.

Note: This doesn't mean you expect to get a $1 bill. In fact, you are only going to get $5 or nothing. But if you repeated this over and over, in the long run the average amount you get is $1.

What's the probability of getting $5?  Are there other possible options?  What are those probabilities? 

We need all of this information to get the expected outcome.

That would be - 5 dollars.

if you get the gift, $5