Your range might actually be too low! I don't see a real reason you couldn't stretch and be competitive in top-20 if your math grades are as strong as your GPA indicates and some of your professors can vouch for research ability (which, given you've received grants, sounds likely).
The GRE scores you've posted aren't good enough, though, and you'd need to retake. It'd be more than fine if they were reversed and you had quant 169 and verbal 158, but with quant that low, your application won't really be considered at most schools in your range. School receive a lot of applications and a lot of them will just do something like "anyone with GRE below 162/3/4/5 goes in the bin". You have time to retake, so you should schedule that asap and aim for 165+ - you have a lot of math, it should be doable.
Most places won't look at five letters (most places won't even look at four without a very good reason), so you should really sit down and figure out which three are going be the strongest for you. This may involve having a very frank conversation with each of your letter writers about how strong their letters will be!