5v to ground using relay but can it be done with mosfet?

I have a few wires that control different functions and have to send them to ground at different times.
The are showing 5v active, whats the best way to use the arduino uno to do this I have been using relays
is there any other way to do this with a MOSFET or something else?

It sounds like what you are describing is "low side switching".

That is where you have power entering a device, then the ground connection leaving the device and going through a switching mechanism before reaching ground to switch the device on and off.

That is exactly how most relays and higher powered LED examples on the web are wired. An NPN transistor of N-channel MOSFET is used in place of your relay, with the Arduino signalling the base or gate via a resistor.

If using a MOSFET, be sure to select a "logic level" one with a low enough RDS-ON at VGS below 5V - typically these have their RDS-ON quoted at say 1.8V VGS

If what you are switching is just a very low current control signal, and not a power signal, you may be able to get away with using the current sinking ability of an Arduino's output port when set to LOW. This can sink up to 20mA (40mA absolute maximum, 20mA recommended maximum), but this should only be used for control signals and never to power anything more than a small LED.

http://ruggedcircuits.com/html/circuit_-28.html is an example

Good example, though I'd be inclined to reduce R1 to say 150? instead of 1K?. The higher resistance will reduce the turn-on time of the MOSFET and cause increased resistance (and hence increased heat dissipation) during turn-on/off times - especially at higher currents. That resistor is only there to keep the inrush current to the gate's capacitance below 20mA.

majenko:
Good example, though I'd be inclined to reduce R1 to say 150? instead of 1K?. The higher resistance will reduce the turn-on time of the MOSFET and cause increased resistance (and hence increased heat dissipation) during turn-on/off times - especially at higher currents. That resistor is only there to keep the inrush current to the gate's capacitance below 20mA.

If you use PWM and the device is switching lots, then yes. For occasional switching I wouldn't worry, the
average device power dissipation will be OK. If you are building from scratch use 150 so you have
the option of PWM

(for very fast switching (high frequency PWM) you need a MOSFET driver chip anyway to get the
switching losses down).