Relay Solution for Controlling Pumps with Arduino
You can use a logic-level gate MOSFET such as the IRLB8314PbF.







simulate this circuit &ndash; Schematic created using CircuitLab

The resistor R2 pulls the MOSFET gate low if the I/O goes high-Z. R1 limits the GPIO current. 

This part has a maximum Rds(on) of 3.2m\$\Omega\$ with 4.5V or better drive, so at 5A it will barely get warm (80mW -> about 5°C rise) even without a heatsink. Only about $1 each in 10's. The diode D1 is to absorb the inductive energy in the motor winding when the MOSFET switches off. It is rated at 3A continuous, which is more than adequate to handle brief 5A spikes.