You need more interval and threshold work. Those will enable you to run faster for shorter distances.
Interval work is done at or faster than typical race pace with long rest intervals. So as an example, since your half marathon race pace is right around 7:00 per mile, that is 1:45 per quarter mile, or one lap around the track. A workout such as 1-2 mile warmup run, 8 x 400m at 1:30 with 3 minutes rest each time would be an interval workout. These are designed to increase your top end speed.
Threshold workouts (fartleks, tempo, all very similar) are efforts slightly below race pace for a longer distance or time, with short breaks. Going out for a run of 1 mile warmup, then 30 minutes of 3 minutes harder effort (Probably 7:20 type pace) with a 2 minute break in between of easy jog. These types of workouts are designed to increase your anaerobic threshold, or the amount of time you can spend at a higher pace.
You've got an excellent base, and 1:30 is a respectable HM time, now you just need the speedwork to break through at the 5k distance.