Lots of good advice from SPG and others here. I'll add some pointers too around what training to do.
5k under 20mins for most people is not easy and will usually take a decent amount of time and effort to achieve. Coming off the back of a marathon this was my next goal and it took me about 4 months to get my 21:08 5k pb down to below 20 minutes (although I managed 19:10 in the end so might have been able to achieve it earlier). You will need to follow some structure and be consistent/disciplined.
5k pace hurts and is not comfortable at all. Usually you will feel like you are dying at 3k and will need to cling on for the last 2k, you will get through it, this is normal
. Getting used to this feeling is very important in your training. First you really need a baseline to build off so get down to a parkrun or something and see where your fitness is currently at for 5k. No point aiming for 20 minutes by the end of the year if you're struggling to finish in under 25 mins. Find out where your at and adjust your expectations in line with that, otherwise you will probably just be disheartened with your training and give up. Ideally you would be below 22:30 at the moment to get below 20 mins in 4 months.
In terms of workouts, I would say the key one for a 5k training plan is kilometre repeats. I'd do these every other week (usually at the start of the week) and start with 3x 1km at goal pace with a 2min walking recovery between. Build this up to 2min jog recovery between reps next time, then increase the intervals to 4x 1km with 2 min walk, then 2min jog next time. Then up to 5x 1km with 2min walk and finally jog the recovery for the last session. Take a longer recovery for the first few sessions if you need to. If you can complete that last workout at goal pace then I would think you are ready for a sub 20min attempt. This pattern works out to be over 12 weeks so plenty of time to slowly build to prevent injury.
You should probably do 2 workout sessions each week so every other week when you're not doing the km repeats do a speed session at faster than 5k pace such as 10x 1min or 8x 400m or 6x 2mins or hill repeats. Basically lots of faster but shorter intervals. The other session can be a fartlek, 20mins tempo, 2x 10 mins tempo, 4x 5 mins tempo, something like that to get you used to longer efforts. Tempo is something like half marathon effort so maybe 4:25 per km?
You need to warm up/down for sessions. I just usually do 5min easy jog before/after.
You will need to do a longer easy run at the end of each week to build up your aerobic base. Start at maybe 40 mins and work up to 90 mins (5min increase each week). Try to fit in 1 or 2 easy runs during the week, maybe around 5k distance. Getting some strides into one of these runs is important too, usually best to do these at the end of the run (these are short sprints at almost full effort and will improve running form). This is 4-5 runs a week.
Fuelling/hydration doesn't matter so much for a 5k. You certainly don't need to drink any water/food during a 5k race, just make sure you've has some food a few hours before. No real need to massively taper your training or anything, just take it a bit easier in the week leading up to the final attempt.
There's a dedicated running thread already with plenty of people with similar goals so have a look in that for tips and help.
, the 80/20 book however is much more sound advice a great book.
and 4k is a slog. 
