No reason why you couldn't lose weight on 5X5...Or I guess I should say body fat, as you are likely to put on some muscle. The 5X5 is meant for strength and muscle gains, but if you're dialed in on your diet and you do the HIIT as recommended above you will lose body fat.
If you're looking to get tone and lose weight, heres a
workout plan for you. You can swap out some of the exercises if you don't have the right equipment.