I'm up to half marathon distance, basically from couch to 13 miles.
I started slowly. I walked on the treadmill to start and kept upping the times and speed until I was jogging. From there, I kept gradually adding distance--as much as I felt I could handle. I didn't try to rush anything, which is why I think I was able to keep at it. I didn't overtax my body; I just kept pushing in small doses.
I ran three days a week (MWF). I might have started out at 3 miles per outing when I graduated from the treadmill to the road (now I do 10, 9, 10 or 8, 12-13, 7). I walked on the off days. You may be feeling good now running five days a week, but if you haven't run before your body isn't going to be up to it unless you're really running short distances. It takes time for your muscles to adjust and for your cardiovascular system to train to the point where you don't get winded. That doesn't usually happen overnight. And resting was part of that. But whatever works for you; the important thing is to keep at it.
Run on your toes. Don't strike the ground with your heel. Your knees will thank you on the long slogs. Taken an id bracelet so the police will know where to mail your body when some idiot driver who isn't watching where he's going knocks you into the bushes. Don't wear cotton anything unless you want to have chafed and bleeding nipples and feet blistered all to hell.
As for body recomp, I haven't lifted weights in three years. I had to start again this week because my upper body muscles have disappeared. My lower body is nicely toned, or at least my woman appreciates it. But such muscles as I show are because I have practically no body fat.