Originally Posted by
burnthesheep
A long sprint and a 15 minute long effort are pretty much diametrically opposed to each other unless you're Wout van Aert. Meaning, you're going to have to pick one. You can improve at both and be mediocre at both, or you can be "competent" at one and really good at the other.
For long sprints or time trial follow the other poster's advice seeking training plans. But just pick one of the two.
I mostly agree, but I think you can improve both aspects significantly if you are starting from scratch. Like in this case the OP might concentrate on longer sustained efforts for the 5 mile TT, but even a handful of sprint interval sessions thrown in alongside will make a big improvement to their sprinting power. For longer sprints (like 1 min), VO2 max intervals would also make a big difference while also contributing to the TT training. So I wouldn't say they are completely opposed goals, at least within reason. There's no reason why the OP couldn't improve both simultaneously. Something like a crit training plan might strike a good balance here.
Having said that I would concentrate mainly on TT training for the segment the OP listed. Sprinting isn't going to help there.