\(5^{x + 1} + 5^x = 150\)
according to the laws of indices
\(5^1(5^x) + 5^x = 150\)

let \(5^x\) = y

5(y) + y = 150
6y = 150

y = \(\frac{150}{6}\)

= 25

but y = \(5^x\) = 25

\(5^x\) = 25 = \(5^2\)

equating powers since bases are the same 

x = 2