2001 Pontiac Grand Am Car started for 5 seconds with no oil

I was changing my oil in the driveway like I always do and had just gotten finished draining the main oil pan, with the drain plug still out I was shimming my way out from under the vehicle when it suddenly started up. My remote start had accidently been engaged while the keys were in my pocket and I somehow hit the "on" button just right. The hood bypass shut-off switch killed the engine about 5 seconds later. I didn't hear any sounds that would indicate damage or smell/see anything. No engine codes were thrown as a result and after filling with new oil and a new filter I started it right up and took it for a spin around the block with no visible problems. My question is, how much damage could I have done in that 5 seconds? Should I be looking to off load the car as soon as possible or should I not worry about it? When I got back from my test drive I lifted the hood and started it again and let it run for about 10 minutes without any incident. I am probably over reacting but I was just curious if any one else had any thoughts about this.