How to create a current/load-dependent dc voltage source?
What you need is called remote sensing in power conversion lingo.

Whatever device you're using to generate or regulate the +5V most likely has some sort of voltage feedback arrangement. This feedback point (or points, if there's return sensing as well) needs to be connected to the point at which you want the voltage to be regulated - that is, at the far end of your power cable. This is done with separate connections from the power lines - usually with thin wires. The feedback node is usually high resistance compared to the load resistance, so that the sense draws only a very small current. This allows the remote sense to be long without dropping voltage due to \$I^2 \cdot R\$ losses.

At the regulator end, you usually put a few hundred ohms between the sense line and the power line so that if the sense becomes disconnected, you still have a point of reference for the regulator.