Questions Regarding 5/3/1 Assistance Work and Conditioning

I can’t do bodyweight dips yet so I’m doing assisted dips with an average Jump Stretch band on my military press day. The thing is, I’ve done dips like this in the past and haven’t seemed to make much in the way of progress. If after the end of this cycle I feel the same way, I’m going to swap dips for another triceps exercise. Close-grip benching seems like an obvious candidate, but I’m doing regular benching and dumbbell benching on my bench press day, so I’m not sure that close-grip benching is the best choice. If close-grip benching is a no go, what would be a good alternative for bringing up my triceps strength to the point where I can do unassisted dips?

As per recommended in the eBook, I’ve picked up a jump rope and starting using it in my warm-ups. Doing it has revealed another area I’m really lacking in: conditioning. The first time, I was a sweaty mess after doing 100 double leg jumps in a few sets and was done doing that for the day. The second time was better, managing to do two sets of 50 double leg jumps, 25 on either leg, and then 50 high knees. I was still out of breath and sweating pretty hard when I was finished, though. My calves were pretty sore after I was done in the gym too, and that was on my deadlift day so I think it’s safe to say that absorbing the force from all the jumps was what did it. Anyway, I’m going to continue jumping rope and get better, but I’d like something else to do to improve my level of conditioning (and lean out a bit more). Given the recent articles on sprinting and the year and half I spent on the track team in high school, I was considering sprints, though not until my second or third cycle so I’m more used to the workload from that. Again, I’m not sure if sprinting is the best choice at this point, so I wanted to ask here first. What would something I could do to improve my conditioning on my off days that won’t interfere with my progress in the gym? (Note: I’m currently a student at a fairly large university, so I’ve probably got a fair number of options at my disposal. There just aren’t any hills to sprint or sleds to drag.)

tl;dr:
Assisted dips not doing much for triceps strength, looking for alternate lift, considering close-grip benching but already doing regular benching and dumbbell benching
Need form of energy systems work to improve conditioning that won’t interfere with progress in gym, running hills and dragging sleds not options

I’d just nix the dumbbell benching until tricep strength improves and do close grips instead.
Can you do at least one dip? If not, do the banded dips and work up to 100 a week- regardless of how you have to do it. Once that happens in 10 sets or less, use a thinner band and repeat until you’re at bodyweight.

As for conditioning- what’s wrong with skipping?
Skip for a half hour a few times a week and you should see a marked improvement in condition. Add a couple walks for recovery and you should be good until you’re sprinting.

push ups…a bunch of them, 5x10 till you can dip and maybe a jump rope?

dips off of a bench or chair, feet on the ground at first

cbgp like you said

reverse grip bp on a Smith machine

push-ups may help, make sure your hands are close together