Remember that [tex]tangent = \frac{sine}{cosine} [/tex].
Since you know [tex]cosx = \frac{12}{13} [/tex] and [tex]sinx = \frac{5}{13} [/tex], [tex]tanx = \frac{sinx}{cosx} [/tex]. Plug the values you're given into that equation to find tanx. Remeber that dividing by a fraction is the same thing as multiplying the inverse of that fraction (aka the fraction flipped):
[tex]tanx = \frac{sinx}{cosx} \\
tanx = \frac{\frac{5}{13}}{ \frac{12}{13}} \\
tanx = \frac{5}{13} \times \frac{13}{12}\\
tanx = \frac{5}{12} [/tex]
Your answer is tanx = 5/12.
You could also do this problem by drawing a right triangle, picking an angle that is not the right angle, and filling in the values of the sides, knowing SOHCAHTOA:
[tex]sin\theta = \frac{opposite}{hypotenuse} \\
cos\theta = \frac{adjacent}{hypotenuse} \\ tan\theta =
\frac{opposite}{adjacent} [/tex]
