Strategy as to when to apply to PhD programs
Your chances getting accepted by applying out of the blue to top institutions is close to zero given that your application doesn't sound particular in any way. Most applicants GPA is between 3.8-4.0 and your GRE scores are ok. Start contacting some specific professors you would like to work with, even if not top-5, even top-10 or 20 will be better if you have a good research connection with a professor. Don't be obsessed with these rankings. If you have free time and money to throw away, sure, go ahead and apply now, but don't expect anything out of it more than the learning experience. You will also not get any feedback from the rejections, so you will never know why you were rejected.