The order of the differential equation whose general solution is given by $y=\left(C_1+C_2\right) \sin \left(x+C_3\right)-C_4 e^{x+C_5}$, is

3

We have,

$y=\left(C_1+C_2\right) \sin \left(x+C_3\right)-C_4 e^{x+C_5}$

$\Rightarrow y=C_6 \sin \left(x+C_3\right)-C_4 e^{C_5} . e^x$, where $C_6=C_1+C_2$

$\Rightarrow y=C_6 \sin \left(x+C_3\right)-C_7 e^x$, where $C_4 e^{C_5}=C_7$

Clearly, the above relation contains three arbitrary constants.

So, the order of the differential equation satisfying it is 3.