Are 5x3 shoulder presses, split squats, deadlifts, and pull-ups enough for strength and size? Would not doing a bench press cause muscle imbalance?
You won't want to do this program indefinitely. It will not result in significant amounts of muscle growth once you get past your linear gaining period. There's not enough volume to elicit a strong hypertrophy response
I would also question why you're doing split squats instead of conventional back squatting. The split squat should exist as an accessory lift, not a primary leg movement replacing the squat. It's not compound enough to be a suitable replacement.
I would definitely include bench press in here as well, I'm not sure what exactly you're asking with that question regarding bench press but, regardless, yes, you should have bench press in here. Nothing else on this plan works your chest in a significant enough way to be a replacement.
This is a high intensity program which would result in strength gains very quickly if you aren't already well trained and adapted to strength training.
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