Well done on getting out the door Nic, 5km is a fair distance to complete and as it's been 3 1/2 years since your last running adventure my advice would be to take tomorrow off and head out again Wednesday?
You may find your next run is tougher due to aching muscles and getting into regular running and obtaining a base level of fitness takes time. Don't rush things, three times a week is more than enough to start and don't ditch the walk breaks just yet, they help you recover during a run enabling you to go further overall before tiring.
If you go back to the opening post you will see how long it took me to work up to running non stop. Everyone is different but please don't rush, it's a marathon, not a sprint.