I have a contract with my job for 1 more year, and I got a better offer to leave now. I gave them 5 month notice. Is that acceptable, or they can refuse my resignation?

It depends. Some labor contracts contain a non-compete clause, which *could mean* that you cannot pursue other employment in the same field for a period, or that you cannot pursue a job with your employer's customers, etc.

Suggest you carefully review your contract's wording... you have the right to quit, but not necessarily accept employment elsewhere right away... if you want to contact me, I'd be happy to take a look and give an unofficial opinion (AM NOT AN ATTORNEY, but was a contractor, and left that employment early and successfully)... I believe you can contact me through the email feature above...