Relay turns on when computer is disconected

However if i disconnect the usb cable from the uno the 5v10amp relay turns on and stays on!

Your wiring shows the 5V pin is connected to the 5V supply, but check your circuit some Solderless bread boards have a break it the two side power bus bars. This is normally indicated by a break in the red and black lines. If this is the case you need to bridge them with a wire.