So here is my little disclaimer; I'm not your doctor. But I have done a lot of physically demanding events & competitions. So take my advice or feel free to shop for better advice. While a 5K is not for everyone, its actually not as bad as you might think and you can work up to it in a reasonable amount of time.

You should start by walking regularly. This applies to pre and post surgery. Start by walking 30 min. I recommend you do this, as much as possible, not on a treadmill. If you need to use a treadmill- ensure you walk on a slight incline to offset the help a treadmill offers you. You should invest in something that can keep track of your pulse while you exercise. Once you can walk for 30 min without issue; you should then start to focus on the intensity of your walk. (Now I should mention that if your weight is still elevated too much, that you may want to be careful with any training. Use some judgement and wait a month or two as your weight should decrease from the surgery.)

Pulse basics
Your heart has a maximum number of times it can beat per minute. As you age this number decreases naturally. You can try and determine this on your own by physically putting your heart to the test for its maximum output. But I don't recommend you try that. I suggest that you follow the tutorial below and estimate your Maximum Heart Rate.

Take your age; I'll demonstrate with age 30.
The number 220 minus your age will yield an estimate of your maximum heart rate.
So for a thirty year old it would look like this: 220 - 30 = 190
For a thirty year old the Maximum Heart Rate would be 190 beats per min.
Take your age and do the same. This is known as your Maximum Heart Rate.

From that we determine a few ranges.
Low end cardio range at 65% Maximum Heart Rate
(220 - 30 =190) 190 x .65 = 123
Take your Maximum Heart Range and multiply it by .65. This will give you your minimum cardio range.
This means that for a 30 year old a minimum heart rate of 123 is where cardio training begins.

High end cardio range at 85% Maximum Heart Rate

(220 - 30 = 190) 190 x .85 = 161
Do the same here. Take your Maximum Heart Rate and multiply it by .85. This will give you the top of your cardio range.
This number represents a maximum target where the exertion beyond this point might not give you much benefit for cardio strengthening. You might not be able to sustain much activity if your pulse stays beyond this point for much duration.

Now you have your range! For a 30 year old, the range is 123-161.

I then recommend that you move to targeting the bottom of your range for a 30 minute session. It might take some time. But each time you keep your heart rate elevated to that rate for extended periods of time you will improve your cardio ability. Once you hit 30 min at your bottom range, try to move up a little bit.

Once you get to that point you are ready to move into 5K training. I strongly recommend that before you begin running that you either get a pose running trainer or spend some time watching tutorials on how to run using the POSE technique. It will help you run without getting injured and give you the best foundation for training. Also, being that most of us are training down in weight ; you may want to ensure you are wearing a stability shoe for running. I know the POSE forum mentions using a flat shoe, but that might not be the best for someone who is training down in weight. If you find you are light enough to wear a flat shoe, do so. But I recommend you be very careful with them. You can easily run into foot and ankle issues if your weight is too high and you use a flat shoe like the Nike Free or Reebok Free Run.

Now it's time to get running!
I recommend using the "Couch to 5K" training regimen. You will need to work out 3 times a week. Best if you skip at least one day between workouts. If it doesn't specify three different work-outs for the week, you do the same workout 3 times that week. There is a "Couch to 5K" training app out there for your mobile device. If you wish to take advantage of that. If not; here it is in a simple workout plan.

Week one
Begin with a brisk 5-minute walk, then alternate 60 seconds of running and 90 seconds of walking, for a total of 20 minutes.

Week two
Begin with a brisk 5-minute walk, then alternate 90 seconds of running with 2 minutes of walking, for a total of 20 minutes.

Week three
Begin with a brisk 5-minute walk, then two repetitions of 90 seconds of running, 90 seconds of walking, 3 minutes of running, 3 minutes of walking.

Week four
Begin with a brisk 5-minute walk, then 3 minutes of running, 90 seconds of walking, 5 minutes of running, 2½ minutes of walking, 3 minutes of running, 90 seconds of walking, 5 minutes of running.

Week five
There are three different workouts for this week. They are as follows:
Workout 1: a brisk 5-minute walk, then 5 minutes of running, 3 minutes of walking, 5 minutes of running, 3 minutes of walking, 5 minutes of running.
Workout 2: a brisk 5-minute walk, then 8 minutes of running, 5 minutes of walking, 8 minutes of running.
Workout 3: a brisk 5-minute walk, then 20 minutes of running, with no walking.

Week six
There are three different workouts for this week. They are as follows:
Workout 1: a brisk 5-minute walk, then 5 minutes of running, 3 minutes of walking, 8 minutes of running, 3 minutes of walking, 5 minutes of running.
Workout 2: a brisk 5-minute walk, then 10 minutes of running, 3 minutes of walking, 10 minutes of running.
Workout 3: a brisk 5-minute walk, then 25 minutes of running with no walking.

Week seven
Begin with a brisk 5-minute walk, then 25 minutes running.

Week eight
Begin with a brisk 5-minute walk, then 28 minutes of running.

Week nine
Begin with a brisk 5-minute walk, then 30 minutes of running.

And that should be a good reference and training model for those that want to 5K. Good luck and hit me with a PM if you have any questions.

This was such a good refresher! Thanks for taking the time to walk us through the max/min heart rate math step-by-step in layman's terms. Especially as the weight falls off and we need to recalculate. It's been a while since I last ran, but I'm so excited to get back to it that I get ahead of myself when thinking of all the 5, 10, 12K's that I want to do in the coming months. I haven't been realistic about how to train to run that first 5K injury-free. Now I have a road map of sorts.

Thanks Emily!
I know some find it daunting. The couch to 5K training is really .. really good. I have a buddy that smokes (on the heavy side too..) and was able to complete the program. Also if the workouts in the training are repeatable. It would be great for someone to take the week one workout and just keep it up for a month if need be. I highly recommend that people get into the pose method for running. It really is amazing and will save your knees and feet and ankles.