Fright Zone
You're sort of describing the bro-split, a 5-day split where each day is a different part. Science has shown us this is sub-optimal btw. Which makes sense. I mean say you fry your back on Monday doing five different exercises, and then you're recovered and ready to work your back again by Thursday, but you wait four more days until Monday to do so, that's a wasted opportunity.
As a beginner, you should aim for 10-12 working sets per week (not incl warmups) per group. And not to failure, although do go close to failure, 1-2 reps away. If you can hit a group two maybe three times in a week, that suggests two or one exercises per part per workout, which cuts down on your time looking for a new machine, then maybe doing a warmup, then finally getting settled in for a working set. This also makes sense, because most muscles only do one or two things. The biceps does elbow flexion. The chest does adduction. The quads do knee flexion. Etc. Sure maybe a certain head of the muscle also connects through the shoulder or hip or whatever, blah blah, but that's getting into the weeds, and you're not a pro bodybuilder.
If you can go four times, then Upper/Lower is good. Some also add in arms and shoulders on leg day, which ofc get a fair bit of work on upper day even if not doing isolations. Three times a week, do full body, though not necessarily the same things each workout, depending on your fatigue.
Look into Starting Strength. It's a very solid program to build a base of strength, which will build muscle too.
The StrongLifts 5x5 training program is one of the most popular strength programs in the gym and our strength expert reviews the pros and cons for your goals.
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Dumbell flys? Is that right? And one where I lay on my back, hold a Dumbell up in my palms and like lower it behind my head - I have absolutey no idea what this move is called?
Yes, fly's. If I had access to cables, I would 100% do those with cables than db's. a) Much better tension curve. b) Less risk of shoulder injury.
And that back one is a pullover. Great exercise. Don't pull it all the way up to vertical above you, that loses all tension on the back and maybe brings in the chest a little, but it's often hard to feel the chest well while doing this anyway.
For chest press, a small incline is ideal, like 15 degrees. It works the middle and lower chest the same as flat bench press does, but it also works the upper chest more than flat bench.
Lastly, I sympathize with the anxiety there. If you can, maybe start up a conversation between sets (never during). Ask them if they can give you any tips. It's irrelevant that they're lifting more. You don't know how many years they've been doing it, how hard they're training, if they're "enhanced", etc. You can only compare with yourself, i.e. progressive overload.