Do you mean you came off Depo 5 weeks ago, i.e. had your last injection then or it's 5 weeks since it should have worn off (about 17 weeks since your last injection)? If it was the former then I'd be a bit concerned about the effectiveness of the injection - definitely ask your GP to take a test, they won't mind at all. When I was pregnant I knew that I was, despite 2 negative readings before eventually getting a faint positive. I told my GP I'd got a positive and he never offered to confirm, just took my word for it! Not sure about whether you can get a false positive, though.