OP, I'm not sure that many miles will do much for the 5k, but this isn't about your training. I suspect that I am older -35- and it can be hard to get out the door for that second run after running in the AM and a full day at the office. I'm understand the caffeine. I do it, too.
3 days a week, I double 8-10 in the AM and 7 after work. I used to get a can of Diet Dew at like 3 and sip on it for about an hour before heading out early for my second run. It ALWAYS made me take a dump and got me ready to run. But the high felt artificial and I never felt great on the actual run. About a year ago, I switched to coffee. I have a great little coffee shop a block from my office, so instead of getting a Diet Dew, I get a small coffee (or a cold brew without ice when it's hot outside), and it does the same thing but it makes my body feel so much better. I also enjoy my run more.
If you take anything away from this thread, it's that you need to ditch the energy drinks. Shit is terrible for you. My guess is that the pros you see drinking them are probably doing it for sponsorship reasons. It wouldn't surprise me if Phelps had water in the can...
Coffee has a ton of health benefits and as long as you don't overdo it, it can be a big help. FWIW, I drink a regular sized mug or two in the morning, and about 8 oz. before my PM runs, so probably less than one Venti at Starbucks. You don't need to guzzle it.
One last thing: if I drink the caffeine, I will go run. If I get a coffee and don't run, I won't be able to sleep, so as long as I get that coffee, I'm locked in to run no matter how bad I just want to go home.