Longest Usable Wires for Low Voltage DC
Given your parameters of 71.4 mA and 70 ohms it appears you are driving a 5 V relay coil. 

You have a choice:


Use a current source to drive the relay
Use a voltage source to drive the relay


My preference would be to use a current source, since this makes it easy to make the solution short circuit proof. 

Perhaps something like this:







simulate this circuit &ndash; Schematic created using CircuitLab

You can select your cable from sites like this, but ordinary telephone cable may suit your purpose, it is typically 20 - 23 AWG and about 1 - 2 ohm each way per 100 ft. Anything below 20 ohm total resistance is unlikely to cause any problems. 

The diode (D1) at the remote end is not required, but some might suggest it.  

The IRF530 should work fine with a 5 V MCU, but if you are using a 3.3 V MCU you would need to select a FET with lower VGS(on) threshold.