Me and my boyfriend have been together for 5 years and the whole time that we have been dating not one day has he shown any affection when we are out in public. But when we are at a couple of our friends house he will love hold my hand and cuddle with me and even kiss me. I am wondering why he can't hold my hand went we are out at places

It took me several seconds to figure out Public Displays of Affection (rather than the usual handheld electronic device).
How? You don't.
Why won't he? A lot of people don't, both men and women. You will have to ask him what his reasons are, but I don't see why he needs to explain. Maybe you need to explain why you feel such a need for it, given that being restrained in public has been the norm in most of the world for thousands of years.
You take people as a package, what you like with what you don't like, and don't try to change them. Be happy that he is affectionate around people he knows. Many aren't even that.

I agree with Joy. Why do you need PDAs?