I’ve never run an 800m, but have run a similar time to you in the mile. My 5k in siginificantly faster though (15:5x).
Clearly you have good basic speed, but you seriously lack enduarmace. I have no idea what your coach has you doing, but I’d recommend building your mileage up a little (to around 30) and doing something like this (basiallly a reduced version of my training)
Monday 4 miles easy
Tuesday 3 miles of speed work
Wednesday - 5 miles easy
Thursday 3 miles of tempo work
Saturday Race; 3 miles of work; or 4 miles easy
Sunday 8 miles easy
Easy runs should be run at an easy pace (just run off feel, no need to look at your watch)
Your sessions and races should include 1 mile slow jog warm up and 4 strides (should take about 10 minutes in total) and finish with 8-10 mins of slog jogging (~ 1 mile)
I would recommend longer intervals for your speed sessions (with long rest to start with) as they will help your endurance, eg. 3 x 1 mile (3’), 5 x 1k (3’), 6 x 800m (2’) etc. Ladders are also good, like 1k, 800m, 600m. 400m, 600m, 800m, 1k all with 2’ rest, or reducing the rest as you go down by 30 seconds at a time and then increasing it back up on the way back up. The rest for your other intervals can be brought down over time.
I’d definitely recommend tempo work. You’ll probably find this is most instrumental in bring your times down. Thing like 3 x 1 mile tempo (1’), 2 x 8 mins tempo (1’) and 3 mile tempos will all help. For a guide, you should be ~25s per mile slower than 5k pace, but you may find that inaccurate because your mile and 5k times differ so much.
On Saturdays you can race, run easy or do a session. I’d you fancy a session, try hill work. Things like 3 x big hills (0.5 mile) and 10-12 x 30s hills. Jogs down the hill should be honest.
Make sure you keep your reps consistent across the board - no starting out way too fast - and report back when you’ve improved!
Best of luck!