Training for a 5k without losing muscle?

Alright, my background: didn't work out at all for about a year. Spent some time in a hospital bed. Lost 10 pounds of muscle, and gained 20 pounds of fat. Wasn't looking so hot even before that so pretty disgusting. Currently have ~15% body fat.

For the past month and a half I've been doing the anabolic diet at a caloric deficit. Losing about 2 pounds a week, while gaining strength back at a decent rate.

Workout consists of (try not to cringe) strictly dumbbells (w/ bench), and HIIT. I'm in law school and at this moment working out isn't high enough of a priority for me to make trips to the gym. It'd be at least 2 hours per workout what with the commute, changing, etc. Weekly I have two days that are chest/legs, and 1 day that is back/shoulders. Probably not optimal, I know. But it was the only dumbbell workout I found online that made much sense. It does involve squats/deadlifts, but of course they're not as good as they would be w/ barbells.

Re: the 5k. There's this running group at the law school, and recently they posted results of their 5k run. Out of curiosity I ran a 5k to see how I stacked up against them. 32 minutes. Fastest guy/girl were 17/21 minutes. Felt pretty bad. Working out alone all the time is getting kind of boring so I'd like to start running with them, assuming I can improve my time well enough get a ~22 minute 5k without losing muscle mass. Body composition is the priority and if I can't do both simultaneously, I'll ditch the running.

Recap/ cliff's notes: 15% bf, currently run a 32 minute 5k, in poor enough shape that I'm gaining muscle and losing fat simultaneously, want to continue gaining muscle while improving my 5k run time down to 22 minutes. Possible or no? Muscle is priority. I know running will hinder that, but to what degree? Thanks.