You have recognised not having made the appropriate adjustment and having being greedy, you already know what to do.
I am 32, 5'11, 228
I am currently doing a 4 day split
Day 1: Bench 1 x 5, press 10 x 1, chinups 3 x amrap
Day 2: Deadlift 1 x 5, squat 1 x 5
Day 3: Bench 5 x 5, press 5 x 5, chinups, 3 x amrap
Day 4: Squat 4 x 5, powerclean 5 x 3
The last two weeks I did 215 x 5 x 5 and 220 x 5 x 5 for volume bench and have failed the 5th rep of 240 x 5. I did jump the weight 5 lbs from 235 x 5 because it went up easily, so maybe the solution is to drop to 237.5 x 5 and then go up 2.5 lbs going forward. Should I move to 2 x 3 for intensity day if that doesn't work?
Should I consider adding close grip bench backoffs to intensity bench or weighted dips to address the inability to lockout the 5th rep?
I don't think this a recovery issue as I am sleeping and eating enough to keep the other lifts progressing, but i could be wrong here
You have recognised not having made the appropriate adjustment and having being greedy, you already know what to do.
Sometimes you just have bad days... I'd go back to 237.5 and retry. If you are stuck and not underecovered, the assistance exercises could increase stress withouth being overwhelming and help progress to resume, but I think its best to be sure whats going on before jamming a bunch of stuff in the program.
You’re doing intensity bench/press on the same day and volume bench/press the same day?
Have you considered splitting that stress differently? IE Intensity bench/volume press on one day and intensity press/volume bench on the other?