I've noticed this as well. I think the reason for a terminal card giving both cards and coin not existing is that cards and coins do sort of the same thing, just with cards being more versatile than coin. When a card gives +cards, it's like giving you potential to do stuff with the other cards in your deck, and when it gives +coin, it's being the card that gives you buying power. +cards is just a way to get to +coin cards (if we're counting treasures as +coin cards); or to get to other +cards cards. Non-terminals do it sometimes because cantrip coin is kind of a distinctive thing (I'm not really sure how to explain why, but it feels different). A card that gives both cards and coin feels like it's trying to accomplish two different things at once, telling you to play through more of your deck but also telling you you're done playing through your deck and it's time to spend. I feel like I did a terrible job of explaining that, but hopefully that made some kind of sense.
Anyway, as for your card, that seems way too strong for $5. Often as a rough comparison, I equate +1 card=+$1 (not perfect by any means, cards are usually better than coin and it certainly depends on the context), which would mean that +3 cards, +$2 is roughly equal to +$5, which is just too much for a $5 card. In big money, if you get this card in your hand you almost certainly can get a province. It might even be too good for $6. If you want to keep it at $5, it could maybe be +2 cards, +$2, or +3 cards, +$1.
I've always wanted to see something like +2 cards, +1 action, +$1, but I'm not really sure how to price that. Clearly it has to be $6, but it might be too weak, since it's hard to grab a lot of $6 cards.
Edit: Also, I thought +2 cards, +$2 is usually the most popular option for Trusty Steed. It seems like it gets chosen more than a third of the time (I'm assuming the silver gaining option is negligible).