Update.

My average times have steadily improved. I've been running 22:xx 5K runs during my mid-week lunchtime runs. I took the advice here and stretched out my Sunday morning runs to 8K distances at about the same pace.

Today I ran my first 5K race and squeezed out a 21:46 (4:22min/km pace)! I'd love to run a sub 20:00 5K run next.