This question seems to come up a lot. I will use power cleans as an example, when you see the program written as 3, 3, 3, 3, 3, 3 that means after you do a skill transfer work on the bar and maybe 2 warm up sets you begin your first set of 3. For example, say your max weight on a 3 rep power clean is 100 kilos, start with skill transfer work like a Burgener Warm Up and then move to your first warm up of 50 kilos where you complete 3-5 reps. Then you go to 60 kilos and perform 3-5 reps. Now you are ready to begin your sets. Your first set is 70 kilos and you perform 3 reps. Your next set is 80 kilos, and your 3rd 90 kilos and hopefully it is all going well. Now you have decision to make, you have 2 sets left and your 3 RM is 100 kilos. Do you shoot for 95 & 100 for your next two sets? Or do you try for a new PR? I would hope you are feeling good, got plenty of rest, had something to eat before you trained and ready to make a jump. So you decide to go for 100 kilos and you complete 3 reps. Now you have 1 set left and you are in new territory, do you take 102.5, 105 or 110? I would say 2.5-5 kilos is a good jump. I would be happy with a 5 lbs increase, but I rather have 10 lbs. Make the decision and go for it. You might fail and only got 1-2 reps but at least you went for the PR. No shame in missing an attempt.
There is nothing wrong with missing a weight or failing on a max attempt. I have been beaten by the weights many times. We actually keep score on this, somedays it is Weights-1, John-0 and the weights get the victory. Other days...a new PR and I get back to even with Weights-1, John-1.
But what if it is written 5x3? That means the program asks you to do 5 sets of 3 reps at the same weight across the board. Say my 3 RM power clean is 100 kilos and the program asks you to do 5 sets of 3 reps at 100 kilos. So do the same work up, skill transfer with the bar and some reps at various weights building up to 100 kilos and go for it. Usually, you will see the notation Set New PR or add 2.5 lbs, that means you should try to do your 5 sets of 3 reps at a new PR, so if my old PR was 100 kilos and it says to set a new PR, then I would complete all 5 sets at 101.25 kilos.
Now that this is out of the way, what about the 5 RM of Deadlift? When it reads Deadlift 5 RM the program is asking you to only pull 1 set of 5 reps at a new PR. Usually it will ask for you add 10 lbs or just set a new 5 RM. Say your 5 RM Deadlift is 100 kilos, I would warm up up the same way as the Power Clean, some skill transfers with the bar then start adding weight. I would pull 1-3 reps for the first few and start pulling singles until you get up close to your new PR. At that point load the bar, step up and go for broke with a new 5 RM. The reasoning behind this is, you fatigue much faster on a Deadlift than a Squat and you only have so many pulls in you, so don't waste them in warm ups. Use all the strength and energy to set a new 5 RM.
For my max efforts I found when I decreased the volume on my DL and ramped up intensity my numbers went up. However, we have contrasting days where volume is high and intensity is lower. This would be seen in dynamic pulling like Power Cleans, Power Snatches and Clean Pulls. We only Deadlift heavy once every 7-10 days because Deadlifts are very taxing on our CNS and can take at least 7 days to recover (I had heard this articulated very well until I sat at dinner with Dave Tate). Sometimes you will see a 5 RM Deadlift and a Deadlift in a metabolic conditioning workout. Usually that is a sub-maximal weight we are asking you to lift dynamically, think high volume, low intensity. Another thing to remember, the metcons are programmed for the Professional level and for strong people so if the weight that is prescribed is 105% of your 1 RM DL, then you need to scale it back. No harm in scaling.
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