The problem asks us to identify which of the given ratios are equivalent to the ratio $1:5$. The ratios to consider are $2:10$, $3:15$, $5:25$, $6:30$, and $10:2$.

1. Problem Description

The problem asks us to identify which of the given ratios are equivalent to the ratio $1:5$. The ratios to consider are $2:10$, $3:15$, $5:25$, $6:30$, and $10:2$.

2. Solution Steps

A ratio $a:b$ is equivalent to $1:5$ if $\frac{a}{b} = \frac{1}{5}$. In other words, $5a=b$. Let's check each ratio:

- $2:10$: $\frac{2}{10} = \frac{1}{5}$. So, $2:10$ is equivalent to $1:5$.

- $3:15$: $\frac{3}{15} = \frac{1}{5}$. So, $3:15$ is equivalent to $1:5$.

- $5:25$: $\frac{5}{25} = \frac{1}{5}$. So, $5:25$ is equivalent to $1:5$.

- $6:30$: $\frac{6}{30} = \frac{1}{5}$. So, $6:30$ is equivalent to $1:5$.

- $10:2$: $\frac{10}{2} = 5 = \frac{5}{1}$. This is equal to $\frac{1}{1/5}$, thus not equivalent to $1:5$. So, $10:2$ is not equivalent to $1:5$.

3. Final Answer

The ratios equivalent to $1:5$ are $2:10$, $3:15$, $5:25$, and $6:30$.