My situation over the last 8-9 months sounds similar to yours --I didn't really run in school (only frosh/soph xc in high school) and then took nearly 15 years off from any running at all. I was still pretty fit, but mainly from other sports and rock climbing. Somehow got into ultras (still not sure how that happened) in 2010 and did that for a few years. Was able to run a 2:54 marathon last fall after burning out on the ultra-thing and have since decided to really focus on shorter road races and see how much I can improve before I get too old and slow.
Since December, I've been able to drop my 5k from 18ish down to low 16s. And I'm hopeful that I'll be able to get faster through club cross country season this fall.
When I made the "switch" last fall from longer stuff, to focusing on shorter running, I immediately went out to the track and started blasting 200s and stuff like that--thinking I needed to run all out on the shorter stuff all the time to get "faster."
But thankfully, I have some pretty knowledgeable running friends who set me on the right path. Running short/fast workouts definitely have their place, but the 5k is still primarily an aerobic event. Pure "leg speed" matters but I'd be willing to bet you have plenty of pure leg speed to break 17 as it is, most people do. Because the 5k (as well as shorter stuff like the mile/3k) are aerobically based, the difference--at least for me--was making a weekly tempo run (usually 8k, but it varies some) the focus workout of the week.
So I'd suggest focusing on getting in a weekly tempo workout, with maybe 6 100-yard strides (on grass preferably) after the tempo. And then incorporate another set of strides into at least one of your easy runs during the week.
Then I would also do an interval session once a week too, but be careful just blasting short fast stuff too often--you'll burn out. Our club often does mixed pace interval workouts, such as 3200 @ tempo, 400 jog, 1600 @ 10k, 400 jog, 2 x 800 @ 5k, 400 jog, 2 x 400 @ 3k w/ 200 jog. And then starting maybe 5-6 weeks out from the goal race, you can start incorporating some real race-specific workouts. For the 5k, that might be 5k-paced 800s-1200s, with some 3k paced 400s/600s for speed support.
Anyways, hope that helps!