Turning a 10A 24V signal on/off with a 5V signal
Use a small transistor to switch a conventional 24V automotive relay, the motors are not a conventional inductive load as the motor driver has freewheeling diodes built in to it to handle the inductive spikes, as well as local decoupling. if anything it would be a slightly capacitive load, but in most cases that helps keep the relay contacts clean. 

Do not forget to include a protection diode in anti-parallel with the transistor C-E, so when the relay spikes when switched off, it does not hurt the transistor.