as a kind of ballpark figure to work with while considering speed for middle distance, I do the following:
1. FAT time over 100m, call this A
2. (2 x A) + 3 = 200m time, call this B
3. (2 x B) + 3 = 400m time (or 4A + 9, same thing)
from the times you have given in your post we see that (15.5 x 2 + 3 = 34), and then (34 x 2 + 3 = 71) which is, pretty much, your 400m time.
also, your mile time of 5:28 is what I would expect off a 71s 400m, your 18:48 5km is also good, but your 10km drops off a little bit (as a rough guide, 10km time = 2 x 5km time plus 1 minute). this tells us that your speed endurance is okay but your endurance could use a boost.
this tells us that your training so far has not induced any weird imbalance in your ability and you exhibit the profile of someone who can definitely benefit from this type of training.
as I am sure you know, training works by inducing adaptations, and those adaptations happen during recovery. as has already been mentioned, speed training depends to a much greater extent than middle distance training on you resting properly both during and after sessions to allow those adaptations to occur. when viewed from this perspective, doing these sessions twice a week is probably not helping.
there are also other things that you can be doing to help improve the effects of the speed work. gym work is really necessary to develop both the muscles required for sprinting and also the structural muscles to help your posture, which in turn helps your running form which helps you run faster. if you are serious about running faster you will need to get in the gym.
if you have not done any gym work before I would suggest you start with some simple circuits. choose a set of around eight exercises, press ups, sit ups, squat thrusts, leg raises and so forth. start by doing 1 circuit of a small number of reps of each exercise and over several weeks increase the number of reps until you can do say 1 set of 10 reps. then cut that in half and do 2 sets of 6 reps and work on building up to 2 sets of 10 reps. at that point you can introduce some light weight exercises (by "light" I mean 25% bodyweight or less), military press, good morning, curls of various kinds and so forth. then do the circuits once a week and the weights once a week for three months at which point you will be ready to start learning squats and cleans.
introduce these at very low weights and concentrate on learning the technique first. as a middle distance runner you do not need to either squat or clean more than 50% your own bodyweight within the first six months and you can make distinct improvement without ever going above that level. remember always that your goal is to run faster, not to lift more. I have attached below a link to a book full of exercises suitable for middle distance runners to give you some ideas. there are other books available but this is the one I use.
meanwhile down at the track...
in your short sprints session use each rep to think about running your fastest during a particular phase of the sprint. the options can include:
1. accelerate smoothly over the first 20m, then hold that speed for 10m, then cruise home
2. accelerate as fast as possible over the first 10m, hold for 10m, then cruise home
3. accelerate smoothly over the first 20m, cruise for 10m, then kick hard for home
the point is that you simply cannot run your fastest over the whole distance, so you need to learn to control your speed. always during this type of work make your recoveries a long, slow, walk back.
your plan to do this after your track racing season is over sounds fine, and that means that you can precede the sprint work with 3 - 4 weeks of hill sprints. you want an uphill slope rather than a steep hill, run around 6 - 8 reps at around your best 400m speed for 150m with walk back recoveries, with a 2 mile warm up and 3 - 4 miles to cool down. you should also at this time be doing some fartlek work mixed in with your easy mileage.
my only concern at this point is that running 10km road races is not the optimum way to improve your mile time, so if your main goal is to go sub-5 for the mile there are probably better things to be doing, but running is a hobby and you must do what you enjoy or it ceases to be rewarding.
good luck, and keep us informed of your progress. if you have any further questions please feel free to ask.
https://www.amazon.co.uk/Strength-Conditioning-Bible-Train-Athlete/dp/147290897X
cheers.