I think that it may be a good idea to drop the weight a little (initially at least), get your 5 reps for 5 sets and build from there. Increase the weight each week, after a couple of weeks it will probably be the case where you get something like 5, 5, 4, 4, 3 reps, but thats fine. Don’t go to failure on any of the sets. Stay on that weight until you get the 5x5. The last rep should be very difficult but not impossible.
Make sure you are getting plenty rest between sets. I wouldn’t do 5x5 on every exercise. If you are training 4 days a week, then you could use 5x5 on your bench press on bench day, squat on squat day and deadlift on deadlift day, and dont bother with it at all on the fourth day. The rest of your workouts could focus on more on some higher rep sets.
eg Bench day
Bench Press 5x5 (rest 2-3 minutes)
Assistance exercises
Barbell row 3x6 (rest 2-3 minutes)
Incline bench 3x8 (rest 1-2 minutes)
Pullup 3x10 (rest 1-2 minutes)
Dumbell shoulder press 3x8 (rest 1-2 minutes) (rest 1-2 minutes)
Be careful to take sufficent rest between sets on the 5x5 exercise. If you take very short rest periods, then of course your reps will drop.
Since you are not used to lower reps then you should be fine for a few weeks on the 5x5 before progress slows.
Poliquins 5% solution is a nice progression and well worth a try. For example take bench day again.
Week 1: Bench press 5x6 100kg (pick a weight that you can get all 5 sets of 6 reps i.e leave room for progression)
So you get 6,6,6,6,6
Week 2: Bench Press (add 5% to the weight) 105kg (drop reps by 1) 5x5
Tricep extensions 2x8
Week 3 : Add 5% 110kg 5x4
Week 4: Jump up the reps. Take a rest from the heavier weights and do a more bodybuilding type routine
Week 5: Use the weight from week 2 with the reps from week 1 (you moght get 6,6,6,6,5)
Week 6: Use the weight from week 3 with the reps from week 2 (You might get 5,5,5,4,4)
Week 7: 115kg 5x4
Week 8: Bodybuilding
Depending on how things are going you may want to try 1 more cycle, but remeber your body is gettin more used to this type of training, so gains will be slower (maybe only up the weight by 2.5 % each week)
Use different assistance exercises (or slightly different set and rep schemes in each 3 week block)
Hope this helps,
Pat