I had a similar problem when I started lifting, for both my dumbbell and barbell presses.
With 5/3/1, using BONEZ217’s suggestions, you might do something like this:
Barbell Bench Press 5/3/1
Flat Dumbbell Press 3x10
One-Arm Flat Dumbbell Press 1x10 (NOT to failure)
Pec Deck 2x15 (light weight, focusing on chest contraction)
Dumbbell Row 5x10
Standing Barbell Press 5/3/1
Seated Dumbbell Press 3x10
One-Arm Seated Dumbbell Press 1x10 (NOT to failure)
Pushdowns 2x15 (light weight, focusing on triceps contraction)
Pull-Ups 5x10 (or 50 total reps)
Make sure your form with the main lifts is very good. That means no excessive leaning back and locking out properly on the standing barbell presses and having your scapulae retracted and elbows tucked (not parallel to your body, but not perpendicular) on the barbell bench presses.
Do not take your 3rd set of the 5/3/1 exercises to failure. Take them past the prescribed number of reps if you know those reps will be easy (often, when people first start 5/3/1, they can get 8+ reps on their 3rd 5 rep set), but stop your set when the weak side starts to lag behind the strong side. If you stop the set when the left side reaches failure, it will eventually catch up to the right side, which is still being worked out, just not to failure.
Remember to do the chest and triceps contraction exercises explosively on the positive and squeeze your chest or triceps at the “top” of the movement. Keep you scapulae retracted and chest out on the pec deck and keep your upper arms still on the pushdowns. You could also do skullcrushers or machine arm extensions.
You can flex the problem muscles after each set, after all the sets, after the workout, or at home later. Since the problem is with pressing, the problem muscles are his pec and/or tricep.
To BONEZ217: I hope I organized your suggestions to fit the OPs 5/3/1 routine template well. I’m familiar with 5/3/1, so I thought I could help fit it together.[/quote]
You know much more about it than I do, so hopefully the OP can put the info to good use.