#### Answer

$5-i$

#### Work Step by Step

Multiplying by the conjugate of the denominator, the given expression, $
\dfrac{26}{5+i}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{26}{5+i}\cdot\dfrac{5-i}{5-i}
\\\\=
\dfrac{26(5)+26(-i)}{(5)^2-(i)^2}
\\\\=
\dfrac{130-26i}{25-i^2}
\\\\=
\dfrac{130-26i}{25-(-1)}
\\\\=
\dfrac{130-26i}{26}
\\\\=
\dfrac{\cancel{26}(5-i)}{\cancel{26}}
\\\\=
5-i
.\end{array}