Answer
$x = \ln 89 - 5$
Work Step by Step
$e^{x+5} = 89$
$x + 5 = \ln 89$
$x = \ln 89 - 5$
Check:
$e^{(\ln 89 - 5)+5} \overset{?}{=} 89$
$e^{\ln 89 - 5+5} \overset{?}{=} 89$
$e^{\ln 89} \overset{?}{=} 89$
$89 = 89$
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