How to tame a rat that hasn't been handled for 4 to 5 months?

Time and patience. You are going to have to reteach her to trust humans. Start just by talking to her not trying to touch or interact in any other way. Rats are social and despite her fear she will want the company. Treats and other food titbits are will help break down the barriers but don't invade her sapce too soon and don't expect over night success. We had one rat (called trigger because he was so fast) in a very similar situation, he used to try to bite anyone who put their hand in or even near his cage. It took several months of patient behaviour but eventually he became a very nice pet, responding to his name and shoulder sitting for a better view of the world. He would still bite if startled (as I found to my cost when he slipped and I reached into catch him)but generally he was as friendly as most of our others.