HA! I really never jogged at all and I smoke to.. really bad combo. Good thing is it gets better. There is a program (for lack of better words) that progressively helps you get to a point where you can job 5 miles. It says in 9 weeks but realistically you can do it at your pace. It's what I have been doing and I'm doing better with jogging and breathing than I was for sure. This is what it works like:
Try to do 3 times a week:
Week 1:
-Brisk 5 minute warmup walk
-Then alternate 60 secs of jogging and 90 seconds of walking for a total of 20 mins (there will be 8 "reps" - walk/job = 1 in total)
-Then 5 minute cooldown (walking)
Week 2:
-Brisk 5 minute warmup walk
-Then 90 seconds of jogging and 2 minutes of walking (8 reps)
-Then 5 minute cool down (walking)
Try this out and let me know if it helps like it has with me. The program is called C25K (Couch to 5 miles) and there is a free app for it on smartphones if you have one. :)