It's a terminal, so what would it look like to play this as the first and only Action card of your turn? Basically:
+2 Cards
+$1
Trash a card (from your hand, you should probably say).
This doesn't seem so outrageously strong that it can't be a $5 card without a penalty. The vanilla parts only add up to a card of Smithy-like power, and while the trashing clearly makes it stronger, the fact that the trashing is mandatory is somewhat of a big deal. I mean, if you don't use the trashing part, it's a terrible card, but it's worse not to play it at all.
Of course, that isn't what the card is. It's "draw up to 5," not "+2 Cards." So it gets stronger in combination with non-terminal hand-size reducers and weaker with non-terminal drawers. (With Village + terminal, it could go either way.) So there are a number of enablers for this card (Festival, e.g.) but actually a bit fewer than you'd think. Just as there are not a huge number of great enablers for Library/Watchtower engines, so also would there not be a whole lot for this. Still, a card being narrow isn't a bad thing, and the fact that it's useful without enablers is a good thing.
So I think my instinct is to say that the penalty probably isn't necessary.