The first thing not to do is panic. Second, check the pH meter calibration. You don't have to re-calibrate. Just measure the 2 buffers. Third, remeasure the mash or wort or wherever you are by the time you read this.
There is no way you should have a pH as low as 5.02. You used distilled water with a small amount of calcium and 3 0z of sauermalz with 12 3/4 lbs of grain. That's 3/(16*12.75) = 1.5%. Your pH should be no lower than 5.45 assuming you used a very acidic base malt. More likely it would be around 5.6. So we suspect the reading. pH readings made in mashes containing sauermalz tend to be alarmingly low initially (yours is typical) but usually increase rapidly and stabilize more or less after 15 minutes. Hence the suggestion that you check again.
pH 5 is really lower than you want but the beer will probably be fine. However if a check of the mash or wort (room temperature - all readings at room temperature) shows a pH of 5.2 or a bit higher that suggests that the mash pH wasn't really as low as 5.0 (except perhaps briefly) and you are fine. Keep us posted.