At the market, Mr. Shaefer sold half of the lychees, which is 1/2*500 = 250
The remaining number of lychees is 500-250 = <<500-250=250>>250
At home, they ate 3/5*250 = <<3/5*250=150>>150 lychees.
The total number of lychees remaining is 250-150 = <<250-150=100>>100
#### 100