$$\eqalign{

& {5^{x – 1}} + {5^{x + 2}} = 3150 \cr

& \frac{{{5^x}}}{5} + {5^x} \times {5^2} = 3150 \cr

& \frac{{{5^x}}}{5} + \frac{{125 \times {5^x}}}{5} = 3150 \cr

& 126 \times {5^x} = 5 \times 3150 \cr

& {5^x} = \frac{{5 \times 3150}}{{126}} \cr

& {5^x} = 125 = {5^3} \cr

& x = 3 \cr} $$