If the distance from the origin to the line ax + by + 5 = 0 is $\frac{5}{\sqrt{10}}$ , then the distance from the origin to the line ax + by + 10 = 0 is

$$\begin{gathered} the dis\tan ce from the origin to \\ the line ax + by + 5 = 0 is \frac{\left|5\right|}{\sqrt{a^2+b^2}}=\frac{5}{\sqrt{a^2+b^2}} \\ \Rightarrow \frac{5}{\sqrt{a^2+b^2}}=\frac{5}{\sqrt{10}} \\ \Rightarrow \sqrt{a^2+b^2}=\sqrt{10} \end{gathered}$$

$$\begin{gathered} the dis\tan ce from the origin to \\ the line ax + by + 10 = 0 is \frac{\left|10\right|}{\sqrt{a^2+b^2}}=\frac{10}{\sqrt{10}}=\sqrt{10} \end{gathered}$$