Navin,
Yes, you can still remain “big” and increase speed.
5k might be pushing it though, as it’s getting “up there” in distance.
I maintain a 210-215lb (5’9") muscular physique while running 12min 2-mile runs. The key is not overdoing the running. That might have sounded crazy, but I’m serious. Your first instinct was correct: you don’t want to run miles and miles everyday, you want to run HARD for short distances once or twice a week.
My favorite are timed 1-miles. Phenomenal for increasing cardiovascular capacity and middle-distance speed, but possibly too short if you’re training for a 5k.
Repeat 400s? Right on. You might try 7x400 with a 200m walk between “reps.” 400s are great. Do that once a week.
Depending on your current level of training your second workout could be 3x1600s (1-mile) with a 10min rest between or something longer like 1x5000m (5k).
Train HARD and train for SPEED. It’s a myth that you need to run long distances to prepare for races. Who cares that your training was 20 miles a week at sub-maximal speed when your competition is based on near-maximal speed for 5 k’s?
The only “secret” is pushing yourself.
Good luck.
-Jeff