If you want to increase your speed your best bet is to do interval speed running. Outside if possible. You have to get your body used to running faster. Best thing is find a track and do repeats - 2 laps easy (usual pace) and then 1 lap all out - recover briefly (walk a lap) and then do it again. Try for 5-6 intervals each workout and you will be cooked. I wouldn't do lift, shake and then run or you're going to be a mighty sick boy. Take the shake after you run.
Since it's only 5k you're running the entire time pretty much flat out but you have to be prepared for it. PM me if you have any questions.
My 5k PB is 19:30 in case you're wondering.