A camel pursue an elephant and takes 5 leaps for every 7 leaps of the elephant, but 5 leaps of elephant are equal to 3 leaps of camel. What is the ratio of speeds of camel and elephant?

Given that a camel pursue an elephant and takes 5 leaps for every 7 leaps of the elephant, but 5 leaps of elephant are equal to 3 leaps of camel.

The ratio of speeds of camel and elephant is $\frac{5}{3}:\frac{7}{5}$

Multiply both sides with $15$

it implies that the required ratio is  $\boxed{\mathbf{25}\mathbf{:}\mathbf{21}}$