A discrete-time LTI system H has impulse response
h[n] = -5δ[n] + 4δ[n-1] - 3δ[n-2].
Use convolution to find its output signal y[n] in terms of its input signal x[n]. Since x[n] is not given, you only need to write y[n] as a linear combination of shifted versions of x[n].