Given that the ratio of $2 a-b$ to $a+b$ is $2: 5$, we can set up the equation:

$$
\(\frac{2 a-b}{a+b}=\frac{2}{5}\)
$$


Cross-multiplied:

$$
\(5(2 a-b)=2(a+b)\)
$$


Expanding both sides:

$$
\(10 a-5 b=2 a+2 b\)
$$


Rearranging to isolate terms:

$$
\(\begin{gathered}
10 a-2 a=2 b+5 b \\
8 a=7 b
\end{gathered}
\)$$


Divide both sides by $b$ (assuming $\(b \neq 0\)$ ):

$$
\(\frac{a}{b}=\frac{7}{8}\)
$$


Thus, the ratio of $a$ to $b$ is:

$$
\(\frac{7}{8}\)
$$