How can I solve this?

3/5 is the sin of the angle you need the secant of. First of all, remember that sin is just opposite over hypotenuse, so we have the opposite side and the hypotenuse, which is 3 and 5 receptively. Now we need to compute the adjacent side, so by the Pythagorean theorem:

hypotenuse^2=adjacent^2 +opposite^2

so

adjacent= \sqrt{hypotenuse^2-opposite^2} = \sqrt{5^2-3^2} =\sqrt{25-9}=\sqrt{16}=4

Now cosine is adjacent over hypotenuse, and secant is the reciprocal of cosine. So secant is hypotenuse over adjacent, and we just computed those, so the solution is just \frac{5}{4}.