I felt exactly the same about my ex boyfriend, he'd want to see me everyday but i just didnt feel like it most of the time, and like yours he was always trying to hold my hand/have his arm around me/something in public and it just annoyed the hell out of me!!
Basically this was happening for a very long time (we were together for 3 years, i felt like this after about a year though...) so in the end i ended it and its the best thing i've done. (and should have done sooner) it just wasnt working out, but i thought in time it would get better again which it mever did.
Im not saying this is gonna happen to you as you've only been together 5 months, but if you dont feel like seeing him now, then is it really going to change? best thing is to talk to him about him and try to work through it or see why you dont feel like seeing him, and take it from there.