This is without doubt the hardest achievement in the game. Reaching 5000 yards is no easy task with luck, or even taking your time with skill jumps. Fortunately, there exists an exploit that will give you this achievement with little to no effort or skill.
Basically the exploit involves using the zoom-out binoculars button in the top right of the screen. What you need to do is start Survival Mode like normal and try and get as high as you possibly can, at least into space (black background). When there, push and hold the zoom-out button. It will zoom-out quite far, and after a few seconds the screen will slowly begin to pan to the right. This is essentially the glitch. Your blob will go off screen, but keep holding the binoculars. To get distance added to your total, rapidly release and re-press the button until your blob is back on-screen. The moment it appears again, push and hold the zoom-out button once again. Remember to be quick here, or you blob can hit an enemy or fall into the water. I recommend holding the binoculars button down for 10 minutes are a time, then tapping it quickly off and on until the moment the blob is back on screen. Then hold the button down again. Repeat until the achievements unlock. In total you will probably need to hold the button down for around 30 minutes. It should also be noted the description is wrong; you are only required to get 4000 meters, not 5000.