I am in my 5th year on L1A visa from UK. Can I apply for my GC now?

No, it's your employer that petitions for you to be eligible for United States permanent residency. Once that petition is approved you may then file for permanent residency. I would urge you to consult with and hire an immigration lawyer to assist you with this case. Not because I think you’re not capable of handling it, you may will be, but in order for the lawyer to debrief and brief you, analyze, assess and evaluate your case in order to maximize the possibilities for a successful result.