What you have now is typical of the UNcabinet professional just plain painter $1.98 faux custom cabinet job perpetuated by con artist builders, typically in TX. They seem to get away with it because no one wants to pay the real costs of durable quality cabinets until it ends up like that and the warranty has run out.

Presumably you want an improvement.

That won't come cheap. That is sanding down to the bare wood and starting over with a professional quality catalyzed varnish in a clean room. 5-7K would be average. Your kitchen would be 7-10K.

Or, reface for around 20K. Or all new cabinets for around 30K. If it could be even be done for that.

5 years of wear will result in an impact chip or two, even in the best quality cabinetry. It should never result in that. That's a coating failure because of a) incorrect prep, b) incorrect products, and c) incorrect application.

Any type of touching that up will just see further chips in different spots. It's chasing your tail. That isn't repairable. That is start over.

You might want to have a conversation with your builder about the low quality cabinets that he provided you. He might not talk to you. He might tell you, tough luck, the warranty is over. Or he might say that he is appalled by that, and have it fixed for you. You won't know until you ask. If bet on the first scenario personally. He has to know that he lowballed you on the cabinet quality.