Can I add 2200µF capacitor to regulator 5V?
You can add the capacitor if you don't exceed the max power dissipation of the L7805. The L7805 is current limited, which means the low impedance of the capacitor won't kill it initially, if the temperature doesn't get too high in the part. This will depend on the input voltage. 

Because typically a big capacitor will cause problems for the load. The L7805 can't source current instantly, the max short circuit peak current is 2.2A, so this is a source resistance of roughly 2.2Ω. This means the time constant with a 2200uF cap is 5 milliseconds which may be a problem if it takes that long to get to 60% of it's nominal voltage on startup for some applications. 

It also means that the regulator needs to source ~2.2A (decreasing exponentially) while the capacitor charges, this may be too much power dissipation if there is a large voltage drop across the L7805.