Could someone please tell me where I can find food for my sylesties? I've searched practically everywhere and I haven't found any.

There is no actual food on sylestia. You just go to either your pet's page and click 'feed pet' and it will deduct a certain amount of gold to feed the pet that day, or go to your stable and click the button that says 'feed pets' to feed all of your pets at the same time. Again, this directly deducts the gold from you and feeds your pets. Later in the game, once you achieve certain goals, you will have access to a stablehand who can feed your pets for you daily. She still deducts gold from you daily to do so, but there's a bit of a discount when she does it (which is a good thing when you have over a thousand pets, like me >>). Hope that helped you out ^.^

Edit: also, other people can feed your pets for you, if they'd like, like I just did for your Keldrind ^.^