Is it normal for men (43M) to not like intimacy?

My husband (43m) and I (33f) have been married for 5 years and we never have sex. I've been trying to find out what is the problem and possible solutions. So far I got: he doesn't watch porn; I'm not ugly; his testosterone was normal last time he got it checked. I'm kinda tired of begging and also tired of been rejected over and over again. Is there a solution? The only excuse I hear from him is that he is tired. Can someone be too tired for intimacy for 5 years straight? Is that an age thing?