Can I use two 7805 ICs in parallel to get double current capacity?
As others have already said, paralleling multiple linear voltage regulators is a bad idea.

However here is a way to effectively increase the current capability of a single linear regulator:



At low currents, there is little voltage across R1.  This keeps Q1 off, and things work as before.  When the current builds up to around 700 mA, there will be enough voltage across R1 to start turning on Q1.  This dumps some current onto the output.  The regulator now needs to pass less current itself.  Most additional current demand will be taken up by the transistor, not the regulator.  The regulator still provides the regulation and acts as the voltage reference for the circuit to work.

The drawback of this is the extra voltage drop across R1.  This might be 750 mV or so at full output current of the combined regulator circuit.  If IC1 has a minimum input voltage of 7.5 V, then IN must now be at 8.3 V or so minimum.

A Better Way

Use a buck regulator already!

Consider the power dissipated by this circuit, even in the best case scenario.  Let's say the input voltage is only 8.5 V.  That means the total linear regulator drops 3.5 V.  That times the 2.8 A output current is 9.8 W.

Getting rid of 10 W of heat is going to be more expensive and take more space than a buck switcher that makes 5 V from the input voltage directly.

Let's say the buck switcher is 90% efficient.  It is putting out (2.8 A)(5 V) = 14 W.  That means it requires 15.6 W as input, and will dissipate 1.6 W as heat.  That can probably be handled just by good part choice and placement without explicit heat sinking or forced air cooling.