I'm sure you know something else that what would feel like an indulgence.
.....
This week, try to run continuously for 2 km. You can do it. Then switch to walking for 1 km, then run 1 km then walk your last 1k=5k. You'll soon be able to run a slow 5 k.
Also, do you have an iPhone? am thinking of setting up a challenge for you!