OP, this is an interesting one to me.
You have a mile time about 5 seconds faster than me, so I'll assume your speed is better. Meanwhile, you run more mileage than me, so I would assume you'd beats my times by more and more going up in distance. But somehow you have a slower 5k than me (I've been just over/under 17 for a few years).
So I would have some questions about your workouts, since you are far from transferring that mile speed to your 5k.
How long are these 6:00/mi tempos you do? I do tempos at about the same speed as you (5:55-6:00 pace), in workouts like 4-5 miles straight. But many weeks I will broken tempos with quite short breaks (e.g. 3x2, 6x1). For the broken tempos I would go quicker, more like 5:45-5:50 or around 10k pace for me.
As well, your overall plan seems like it could easily lead to a plateau if you don't mix things up. Rather than just doing 6x1k on race pace week after week (with what recovery, by the way?), try 6x800 or 4x1000 at 3k pace (2:00-3:00 rest). I found that running more intervals faster than 5k pace (at 3:15-3:20/k rather than 3:25/k for me) made a difference for all of my events. Like the guy above said, start thinking of 80s/lap as your baseline zone - you are fast enough!
I hope that you post back about how it all goes.