It depends on what you are meaning. If you mean you have studied for 5 months so that you could do something, e.g., taking a test, and that you have stopped doing so since then, then I imagine the first sentence is more appropriate. But if you mean that you have studied for 5 months and continue to do so, then you should use the last sentence in the present perfect continuous, for it expresses an action that has been happening during some time and still happens.

I imagine you already know the difference between the present perfect and present perfect continuous in English. You can apply that knowledge here, however, the difference is not that crucial for the verbs to study, to work, and to live. I believe that this is due to these verbs' not being exactly verbs of action and not being exactly verbs of state.

I´m learnig English... but I think it´s depends if You are studing or if You finished your study....If You finished, the first one if not the nd one....