I'm going to assume from your statement that you herniated your L4/L5 disc that what happened was you began experiencing back pain, went to see a health professional of some kind, and they referred you for imaging (X-ray or MRI), the result of which was the detection of a bulge in the L4/L5 disc. If that's not the case, please let me know as that may change my answer.
If that is what happened, here's the thing - you don't know for sure that this is actually the cause of your pain, because you don't know whether this imaging abnormality was there (but asymptomatic) before you had pain, unless you randomly happened to get a back MRI earlier, when you were ok, and that first MRI showed that the disc bulge wasn't present then. Now, that might seem strange, because you'd really expect to be in pain, but it turns out that these type of spinal imaging findings (herniations, bulges, extrusion, and everything that used to be labelled "degenerative disc disease") and actually extremely common in people without back pain. 37% of healthy, pain-free 20 year olds will show disc degeneration on an MRI, and this increases with age to 96% of 80 year olds1. So the problem is that if you experience back pain, get an MRI and it reveals evidence of "disk degeneration", the chances are really high that it was actually there before you started experiencing pain, and is actually completely unrelated to your pain experience. For this and other reasons, international clinical practice guidelines are consistent in recommending against the use of routine imaging in the diagnosis of back pain2, instead recommending it only when there are reasons to suspect the pain is caused by a more serious problem, such as cancer or spinal fracture. Unfortunately though, many doctors are not up to date with these recommendations and still refer back pain patients for imaging which can easily lead to incorrect diagnoses, and even direct harm.
With that in mind, hopefully the concern about putting pressure on spinal discs (which is unavoidable in any kind of back exercise) won't be such a concern, and I'd suggest you move forward by experimenting with what kind of exercise you you do without causing your symptoms to worsen. This can be achieved by any combination of reducing the load on the exercises you want to do, reducing the range of motion, or selecting different exercises, and then very gradually working back towards the type of training that you would like to be doing if not for the back pain.
Here are a couple of excellent resources on this: