Is there a path to residency for me if I came to the US legally on a visitor's visa when I was 5?

Generally, a foreign national who entered the U.S. lawfully and with inspection, such as entering with a visitor's visa, and who later becomes married to a U.S. citizen, can succeed in a marriage-based adjustment of status application to become a Lawful Permanent Resident (to get a "Green Card"). This is true even if the foreign national may have long overstayed the initial visa. Of course, there are many other details that have an impact upon eligibility. It would be wise for you and your fiance to consult with an immigration attorney who, after learning all of the relevant details, could advise about immigration eligibilities, options and strategies, and then could offer legal representation in the often complex application process.