5x5 Shoulder Press + 3x3 Bench Press + Cathedral Stairs

WODs
5x5 Shoulder (strict) press
85-90(3,F)-85-85-85(4,F)
I was able to get 90 up five times on December 4, but that's okay. My current 1RM is 105. My chest/lats/whatever was a little sore from burpees/knees to elbows yesterday. I fought with the last rep of set 4 for about 20 seconds, literally.

3x3 Bench Press (flat bench)
115-125-135(1,F)
I think I'm going to add the bench in a little more, despite the fact that I think it's silly. It also has the problem of needing a spotter (which none of the other movements really do), but hopefully I'll be able to work it out.

My chest just isn't that strong and the bench press seems like a reasonable way to work on that (in addition to doing more push-ups). I'm told this will help with overhead strength as well.

I'm considering doing something like Jim Wendler's 5/3/1 program. One of the movements is a bench press (along with shoulder/military press, deadlift and backsquat). My goal is to be able to bench my bodyweight 3 times (it's currently my 1RM) and I'll go from there.

Cathedral stairs (37 floors) for time
5:15
I've run cathedrals before, but I've never timed it. This was pretty miserable. The stairwells are so dry, I'm still feeling the effects in my chest (now ~7 hours later).

Skills
PVC pipe snatches
PVC pipe overhead squats
Push-ups, one-arm push-ups
I attempted the one arm clap push-up... not happening but I know it's possible so I'll keep working on it