Well I don't really see how walking or running 3 miles would make a difference. An inch is an inch, a meter is a meter, and a mile is a mile wether it's walked or ran. Kind of like that question which is heavier a pound of feather or a pound of bricks, it doesn't matter because it's still a pound.
As for running a 5k I just started running less then 8 weeks ago I think and I just came home from my first 5k ever! I couldn't run the entire thing but I'd say I ran about 2.5 miles of it at least. My time was about 37:12 to complete it though I may be off by just a few seconds since I didn't get to see the official results list yet. I've been using the couch to 5k program and love it! I also have lots of weight to still lose but I'm truckin along lol. You can do it good luck!