I had look up the Dirty Dash. I figured it was a "muddy" obstacle course similar too the Tough Mudder, Warrior Dash, Spartan Sprint, etc.
How do you train for it ? First off, can you run five miles ? If you've never done any sort of distance running, you should start with a Couch to 5K program. SP has one. A C25K assumes no prior running experience and will literally take you from your couch to a 5K road race. A 5k = 3.1 miles. That will get you started. AND before you start your running training, I would encourage to you get fitted for a proper pair of running shoe. Don't wear any old shoe. If you're going to run, your feet will need proper support. Thus the need to wear properly fitted shoes. Wearing the wrong shoe can cause problems with your feet, ankles, knees and hip joints. So, do go to a reputable running/sports store to be fitted for a decent pair of shoes.
Now, what sort of strength training have you done ? If you want to be able to do an obstacle course, that's going to require some upper body strength as well as some core strength. However, let's start small. How many push ups can you do ? Being able to do good military style push ups will help you complete one of these obstacle courses.
check this out for push up training hundredpushups.com/
Hope you enjoy burpees ! Those will help too. I loathe them. www.youtube.com/watch?v=Pf7wZvraWV0
Start slowly. if the Dirty Dash website is correct, you have until August to train for this five mile obstacle course. Are you too old ? I was 48 when I did the Spartan Sprint.