The iPod Touch 5 carries a Retina IPS LCD display of 4″. The replacement part is specific to that panel, which is why the price you see is for this exact model and not an average.
A iPod Touch 5 Screen Replacement starts at $135.99 at verified shops in Miami, FL. The final price depends on your exact model — you see it before you commit.
Yes — every shop is verified and you see its warranty terms before booking.