Apparently your relay has a coil that takes +5 V and Gnd and 3 other terminals if it is a double throw. The center terminal connects to the NC (nomally closed) pin when the power is off and it connects to the NO (nomally open) pin when the coil is energized. To connect a spindle, you would cut one of the power wire and connect one side of the cut to the common and the other side to the normally open. When the coil is energized, it will switch and turn on. You can connect the fan the same way to the same power source if the relay is rated with enough amps to switch enough power for both.
Use the Gnd and 5 v to “power” the relay. The Aux is the switched power line from the controller that changes when the relay is to be turned on. The aux line switches the 5V line to energize the relay when using a relay like this one:
An optically isolated circuit is provided on the relay above to keep the Aux microcontroller pin signal away from the relay to avoid frying the microcontroller. If your relay does not have an opto-isolator or a transistor circuit to switch the 5V, you “can” try the microcontroller line direclty, but it is not recommended because the relay current draw can be too much for the micro causing it to brown out and reset or overheat that circuit inside the chip and let the smoke out, so be careful.