Can you give some more information, What pace are your long runs at, what kind of speed work at 5k pace?
If I was training specifically for running, the week would look more like this
1 long Run, 70-90min W/20-30 @ Just Above Half Marathon Pace
1 Tempo Run 60min W/ 24-40 @ 10k Pace
1 Strides Run 50min W 1-3minx6 @ 5k Pace
3 EASY Runs 50min
1 Recovery Day
These have ranges that you scale as you progress towards the race.
Dunno if it’s an every week kind of run, but I’ve really started enjoying (after the fact, of course…) 2x20’ with 10’ easy in between.
I find that my workout 20’ pace is pretty close to my 13.1 race pace so for me it’s an indicator in addition to being a solid workout.
Fair warning, and call it a brag if need be, but with warmup and cooldown, this can turn into a 12+ mile workout.
Can you give some more information, What pace are your long runs at, what kind of speed work at 5k pace?
If I was training specifically for running, the week would look more like this
1 long Run, 70-90min W/20-30 @ Just Above Half Marathon Pace
1 Tempo Run 60min W/ 24-40 @ 10k Pace
1 Strides Run 50min W 1-3minx6 @ 5k Pace
3 EASY Runs 50min
1 Recovery Day
These have ranges that you scale as you progress towards the race.
This sounds super solid. How far about half marathon pace are you going on your long run? Sounds very close to just racing. If race pace was 7:00, would long run be 7:10s? 7:30s? 8:00s?
My opinion would be that you are running two much in the “grey” area. ie. your “tempo” (if it is your true intention) run needs to be faster, you want to run a half at 6:30 pace but you are doing very little work at that pace. Don’t be afraid to run 8:30-9:00 minute pace some days in order to facilitate running your tempo run at 6:30 pace.
The ladder you posted is a great workout, but I would suggest you bring that below your five k pace, and truly make it speed work.
Its not the entire run just 20-30 minutes close to the end of the run, so if your race pace is 7:00, of the 90 minute run the last 30 minutes would be around 7:10 pace.
Ah…that whole “reading” thing. Makes perfect sense.
“It would be tough for me to do the ladder workout faster than 6:00 pace, especially the mile in the middle. I could handle 400s and 800s at sub 6 pace right now, but probably not anything longer unless I took a full recovery equal to the interval time.”
It’s not supposed to be easy! 
It may be that you cant but maybe rather than jog in between it becomes 1 minute walk 1 minute jog, or a full two minute walk. As well something that worked for me was to build up to ladder workout work on SPEED. so given your current 5k time your speed work would look a bit like 6-8x400 w/200 recovery, try to run the 400’s on 1:20-1:25, 6-8x800 w/400 recover, try to run 2:50-3:00. Its going to be hard but it will improve your ability to run fast.
I do not worry about any of this fancy stuff. Get out and run 3 to 4 days a week. do lots of hill work… Lose the weight. take years of this to improve w/o getting hurt.
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