Digital switch to handle 5v 2A?
There are certainly many MOSFETs that might be able to work for you. High-side switching at the same supply voltage as your control signal can be accomplished by a P-channel logic-level MOSFET. 

Here is a typical circuit. R1 adds some isolation to the MCU and slows the switching a bit to reduce EMI, R2 ensures that the MOSFET turns off fairly quickly if the input becomes disconnected (the MOSFET can get very hot and damage itself if partially on) and D1 deals with inductance that may be present in the load. The MOSFET is a small SMT type (virtually all suitable logic-level MOSFETs will be SMT type)







simulate this circuit &ndash; Schematic created using CircuitLab

The MOSFET circuit requires about as many parts as the relay circuit, however you would have to assemble them yourself, including the SMT MOSFETs. The relays have a number of advantages- the module is already assembled and perhaps even tested, the relay contacts are robust and can withstand surges (voltage and current) without immediate catastrophic failure, and the contacts are completely uncommitted- you can use them to switch high side, low side, 12V or 5V, AC or DC, whatever you like. If you decided to do low side switching with the MOSFET you'd have to use a different type (N-channel). If you wanted to switch more than 5V high side, you'd have to add circuitry to level-shift the control. So it does tie you down a bit. 

Disadvantages are noise, bulk, some arcing, and limited life (typically life rating is 100,000 operations at full load current so you can wear them out in days if you switch them frequently). Power consumption is typically 360mW for that type of relay (I didn't look up your specific ones), but contact losses will be almost nil. The MOSFET I mention might lose 120mW at 2A when hot, so less. In the latter case the loss comes from the load rather than the coil current.