Is your user name really "Iron Anus"?
As the title suggests, why do we do sets of 5 for volume on programs like texas method and HLM? I get that on the texas method, the trainee needs to be recovered for friday's heavy sets so a monday volume day consisting of 4x12 squat would be a bad idea most likely. However, on an HLM routine, the heavy day is done at the start of the week so this consideration becomes less important. Wouldn't doing more than 5 reps per set be a better option for a volume stimulus as this would build more muscle than a 5x5?
Is your user name really "Iron Anus"?
I'm more interested in why not less reps with more sets. Seems that one will be able to use more weight with less recovery time between sets = more volume in the same amount of time.
It's been written about in The Book, p. 301-303. PPST3 also mentions this on p. 61-63. It's the most useful rep range for the novice, and while the intermediate becomes less reliant on 5s for building strength, it's still important. Likewise, the advanced trainee would be well advised to use 5s from time to time in order to build plain old strength.
Sets of 5 is a good starting point, but it's just a template. When you begin to learn how you respond to different stimuli, you make changes to your programming. This is where the logs here are a valuable asset. Take some time to look through the logs of people that have been lifting for some time and you will see many different variations on volume work.