We've been living together 5 years, filled taxes together as married, presented ourselves as married. Now he moved out of the house that is in his name, and now wants to shut off utilities and kick me out. What's my rights.

You have the right to contact a family law Attorney and find out what "he" can and cannot do. You will undoubtedly have to file for divorce.

CO does recognize common law marriage. http://www.state.co.us/gov_dir/leg_dir/olls/pdf/common%20law%20marriage.pdf

At the very least you are a tenant in the house. As such he cannot cut off the utilities or kick you out. This would constitute an illegal eviction which you can sue over. To evict you, he would have to do it formally according to local laws.

But I agree with Judy. I would consult a Family Law attorney to determine what rights you have in dissolving a common law marriage.

I didn't mention that Colorado is a common law State - appeared the OP already knew. That's why I said "divorce."