I think the time depends not only on the person but also on the type of therapy. Some approaches (e.g. CBT) work in a way that it's focused, specific goal oriented, and is designed to give the patient a specific set of tools then let them go. Others (e.g. psychodynamic or psychoanalytical therapies) are usually less focused on one area and attempt to deal with a broader range of issues including figuring out the underlying mechanisms -- these will obviously take longer.

I think some people also remain in therapy long term for maintenance, much like having a gym membership and exercising for the maintenance and open-ended improvement of health. Some also try a few different approaches and therapists before truly experiencing benefits and that takes time as well.

It's hard to predict what you will likely experience in the next few sessions but 5 sessions should definitely be enough for you to get a feeling.