x/50-8=x/60+5

x/50-x/60=5+8

x/50-x/60= 13

60/300x-50/300x= 13

10/300x= 13

1/30x= 13

x= 13*30

x=390

Xiaoming's distance from home to school is 390 meters.

Analysis: This is a typical profit and loss problem. To solve this problem, we must first adopt the mathematical model of "equation". According to "S=VT", "T=S/V" can be obtained. If the distance from home to school is x m/s, then X/50 is the time that Xiao Ming needs to spend on the road. He is 8 minutes late, so subtracting the extra 8 minutes is the time that Xiao Ming should spend on the road. Similarly, X/60 is the time needed for Xiaoming to shift gears, and he arrived five minutes early. These five minutes add up to the time that Xiao Ming should spend. So we can get the equation: X/50-8=X/60+5, and the result is X=390.