Just stick with the program. You will not be doing 20+ reps of your top set forever. Don't adjust your TM other than the prescribed increases each cycle (2.5kg for the bench/press, 5kg for the squat/dead).
It will take time for your body to adjust to the heavier weights, so that's why your 5+ week you're getting 20, but on the 1+ week you're getting 4-5. Also - take your deloads every 2 cycles. If you cannot hit 5 reps on your TM, your TM is too high, so if you're only getting 4 reps on the 1+ set, your TM is too high.
The point of taking a deload is so that you never need one. If you can't hit 5 reps on the 1+ set on 5/3/1 week, you're not recovering well, and you need to deload, or your TM is too high.
Since you're new to the program, you may want to try something like this:
2 Cycles of:
5's pro + 5x5 FSL
50-100 abs/single leg work
followed by 1 cycle of
5/3/1+ PR set
50 abs/single leg work