Just go jogging / running around the neighborhood or lake or park. Try some to do 2 days of wind sprints (try to do 5-10 sprints on those days with 1-2 minutes break between the sprinting). Remember it's a sprint so you are suppose to go all out for 50-200 meters.
As for no weight workout try this, go nonstop from one to next but do: 50 pushups, 50 crunches, 50 squats. Try doing 1 set, then if you can take a 2-3 minutes break and do another set. If you can go up to 3-5 sets, try upping it to 75 reps instead of 50. Once you can get to 100reps at 5 sets, you are wayy ahead of the curve. If you can jog 5 miles nonstop you are sitting pretty as well, try to make that a goal. Once you can do that, then increase your speed and decrease the total time to do that 5 miles. You really dont' need to hit the gym for first month of training to get the body ready BUT the gym will greatly help your body prepare.
good luck on the journey, stay healthy and fit.