1st advice: don't pay much attention to GFY advice
See, the thing is that every body, every condition, every health is completely different. As an example, I exercise 4-5 times a week, and I do 15-20 minutes bike every day.... yet I wouldn't be able to run the distance you want to run. One of the reasons is I'm pretty muscled (hence heavy) and I was a basketball player, hence my ankles are shit. Plus, I smoke 12-16 cigs a day. Thus, I run 200-300 meters and I have to slow down. After 20 mins of jog/walk/jog/walk I cover around 5km and I feel a step closer to sudden death
My wife never ran and she started going to the gym 2 months ago. She jogs 30-40 minutes every day, then goes to some gym class or spin bike class.
A friend going to the same gym runs 1 hour at full speed. A trainer at that same gym can't even run, he can barely walk!
So, my point is that you should discover your rhythm, what can you do and what you can't. Plus, it's not the same running down the street that having runner's paths or running on a treadmill.
If you want to try, just do like some people already said: start WALKING, then add some speed, then walk again and so on. Just be sure to take the time you can jog and add 15-30 seconds a week for the jog interval. That way you'll probably be able to jog the entire distance in a couple months