I wouldn't really worry about this; 5k isn't very far at all.
If you wanted to be more primal about it, try a sort of military power march i.e. jog/slow run for a certain time or number of steps, then fast/power walk for the same time/steps (if you are feeling really tired, increase the walking bit; if you are feeling good increase the running).
Im with the idea of walking if you can't run. mix it up a bit. why not walk up the hills and run down the hills and the flat bits maybe. I can run all day on flat roads..chuck in a gradient and I start to falter
Caution! My replies may contain traces of nuts!. My posts are just my opinion based on my experience with the primal way of life, there is no assurance it will work with others in the same way.
Started Primal 15th October 2012
Start weight 200lb
Loss so far 33.8lbs, now 166.2lb
Goal was 168lb's
Why don't you start running ... and after a few hundred meters or so you pretend your knee hurts or whatever so you walk the rest of the race ? Yeah, that would be a lie but so what ?
Just start out running and when it doesn't feel good walk for awhile...then repeat till the end of the race. Walking is the most natural exercise of all with running slowly the 2nd most natural. No reason to give up running in your every day life just slow it down and run in a stress free place you enjoy...like a park or the woods.
You could try the couch to 5K. I'm assuming you've run before, so it shouldn't be difficult to do it faster than 9 weeks. If you find the first workout too easy, skip to week 2 and so on. That should prepare you in a month.
If you don't want to run, don't run. I spent 25 years running long distances, doing well over 100 races from marathon to 100 mile distance, and hundreds more below the marathon. And then, I decided I'd had enough. After averaging about 150 miles per month for 25 straight years, I pretty much walked away. Last year, I didn't make it to 100 miles for the year, and almost all of those miles were done as sprints or an occasional slow jog with the dog.
I get asked by my running friends all the time when I'm coming back to doing marathons or ultras, and I simply tell them I don't miss it right now and I don't feel like running.
Last night, I did a one mile time trial after a CrossFit workout and I was almost 3 minutes slower than my best mile time from many years ago. And, I was fine with that.