For now, 10K
I am currently capable of 5K but puts a lot of stress on me.
That sir, is truly my area of speciality. I used to be a marathon runner, and intend to start running marathons again from 2017.
Ideally, the best training for running....is running. But, there are different kind of runs, and each of these should be part of your training.
Session 1- Run to your longest distance. Normally on the weekends, choose the longest distance you possibly can and add 10% the next time you run it. So, if the max max you can run this weekend is 5k, run another 500m next week. And another 500m the week after. Of course, make sure you dont get injured running that extra 500m, but even if that extra 500m means running a lot slower than your average pace, thats fine. And at least give yourself a day's break after this run.
Session 2 - Since you are only running 5k now, try another run during the week of around 5k, but not more than that. As your fitness starts improving this run should start getting faster and faster. If you do 5k now in 45 mins, 3 months down the line you should be running 5k in 35 mins.
Session 3 - Try a quick High Intensity Interval training session - So sprint for 100m, then a nice easy jog for another 500m. Do this 3 to 4 times. As your fitness improves, you could elongate your sprint distance and do a longer session.
Session 4 - If your knees and joints allow - do Squats, Lunges and Planks. You do need to have access to a gym and can do it without any weights at any corner of your home.
1 sets of Squats - 10 reps each
1 sets of static lunges - 20 each (10 for each leg)
Plank - Start with 15 secs, and try adding 5 secs every week.
And repeat each of these 2 more times (3 in total) to perform a superset. Take 1 mins rest between time you finish the 3 exercises.
This session should not take you more than 20 mins. If you cant do 10 reps, then just do as many as you can work on increasing the number of reps one by one. Obviously, dont push if you have joint/knee issues.
If you perform the above sessions and workout 4 times a week, you would be running 10k within 3 months. I understand that working 4 times a week is difficult, but that is the minimum amount of time I recommend that a person workout if they want to see a difference in their fitness. Your body is most valuable thing you have.
One of the things that works best for me is to sign up for a run in advance. For instance, if you really want to motivate yourself to run this 10k, sign up for a 10k event which will take place after 3 months.