$2^{x + 1} \cdot 3^x = 5^{x + 3}$
$\ln \left( 2^{x + 1} \cdot 3^x \right) = \ln 5^{x + 3}$
$\ln 2^{x + 1} + \ln 3^x = \ln 5^{x + 3}$
$(x + 1) \ln 2 + x \ln 3 = (x + 3) \ln 5$
$x \ln 2 + \ln 2 + x \ln 3 = x \ln 5 + 3 \ln 5$
$x \ln 2 + x \ln 3 - x \ln 5 = 3 \ln 5 - \ln 2$
$x \ln 2 + x \ln 3 - x \ln 5 = \ln 5^3 - \ln 2$
$x (\ln 2 + \ln 3 - \ln 5) = \ln 125 - \ln 2$
$x \ln \dfrac{2(3)}{5} = \ln \dfrac{125}{2}$
$x \ln 1.2 = \ln 62.5$
$x = \dfrac{\ln 62.5}{\ln 1.2}$
$x = 22.68$ answer