Go with what your DSO said. They are the one who will request to reinstate your SEVIS status. No you won't need a new visa. First, you are still in the US, with a lapsed status or not. Unless you plan to leave the US, you won't need a new visa. The 5 months period refers to your being out of country as well. Sometimes, student will take a year leave and ask the school for a deferral and the DSO to suspend their SEVIS status. When they are ready to come back to the US, they must apply for a new visa, regardless of whether the old visa is expired or not.
In your case, since you are already in the US, you will just need to make sure your I-20 is current and SEVIS is current. Only your DSO can help you with both.
Important Notice: My opinion is just that, my opinion. It is not intended to be used as Legal Advice. I highly recommend you to seek legal advice from a competent immigration attorney. When possible, I may submit an outside link as source. Please use your judgment to determine if the link is useful or truthful or not. Last but not least, good luck in your journey to America.