Let Xiao Ming's original speed be x m/min and Grandpa's speed be y m/min.

25(x？ y)=35003500？ 5y=20(0.5x+y)，

Solution: x = 200 y = 60.

So the distance from Xiaoming's home to the gym is: 200×25=5000 meters.

So the answer is: 5000.