Can't help you with 5k pace predictions.
3k pace: I did 5 x 1k in 3:12 with somewhere around that amount of rest and ran 8:58 for 3k a few days later (2:59 1k pace). I felt like absolute ass during the workout but even on days where I felt good I had trouble averaging 3:05 and I'm not sure I ever completed a 5 x 1k workout at that pace. So I'd put your 3k at 8:30 - 8:40 (1k rep avg minus 8 seconds per 1k so you should be able to average 2:50 per 1k for a 3k). Start conservative at 2:53-2:55.
In my 3k PR I ran 3:29 for first 1200m, died a little in the middle (was at 5:57 for 2k), then hung on with a modest kick to get to 8:58. With better pacing I probably could have run 8:55.
A better predictor for 3k pace in my own situation was 5 x 600m with 200m jog rest. On my best day I averaged 1:42 (68 pace), so that would be about 4 seconds per lap faster than my 3k pace. I think I was jogging the 200m in about 53 seconds on average.