Answer
$7$
Work Step by Step
Let $x$ be the number.
The conditions of the problem translate to the equation
\begin{array}{l}\require{cancel}
\dfrac{13-x}{8+x}=\dfrac{2}{5}
.\end{array}
By cross-multiplication and using the properties of equality, the equation above is equivalent to
\begin{array}{l}\require{cancel}
(13-x)5=(8+x)2
\\\\
65-5x=16+2x
\\\\
65-16=2x+5x
\\\\
49=7x
\\\\
\dfrac{49}{7}=x
\\\\
x=7
.\end{array}
Hence the number is $
7
.$
