Ok so here is the deal... I’m not a pro runner by any means. I have a 16:27 H.S. pr haha. But I think I do know enough to help you out.
My personal opinion is that speed work is NOT needed until you are breaking about 18:00-18:30. You can get in sub 20 shape pretty quickly by doing long easy runs (for you this would be 5-8 miles) and tempo runs (go for 2-5 miles at a pace that hurts but doesn’t kill you)
Doing 250s won’t be very beneficial for you, depending on intensity that’s more in the
400-1600 training zone.
If you really do have an itch to scratch for speed work I’d hit the classics for my XC Team:
3-5 Mile repeats at goal 5k pace with a rest time equivalent to the mile time.
6-10 800s at slightly faster than race pace (think about 2:55 - 3:05 for you)
Or 400-800-1200-1600 ladders at faster than 5k race pace.
Running up and down a big ole hill works too.
I wish you the best of luck! My first time breaking 20 was very satisfying and one of my proudest races to date :)