To find the value of tan(alpha), we can use the identity:

tan(alpha) = sin(alpha) / cos(alpha)

Given that sin(alpha) = 5/13, we need to find cos(alpha) to calculate tan(alpha).

Using the Pythagorean identity:

sin^2(alpha) + cos^2(alpha) = 1

We can substitute the value of sin(alpha) into the equation:

(5/13)^2 + cos^2(alpha) = 1

Simplifying the equation:

25/169 + cos^2(alpha) = 1

cos^2(alpha) = 1 - 25/169

cos^2(alpha) = 144/169

Taking the square root of both sides:

cos(alpha) = ±12/13

Since cos(alpha) can be positive or negative, we need to determine the sign based on the quadrant in which alpha lies.

Since sin(alpha) is positive (5/13), alpha must be in either the first or second quadrant. In both quadrants, cos(alpha) is positive.

Therefore, cos(alpha) = 12/13.

Now, we can calculate tan(alpha):

tan(alpha) = sin(alpha) / cos(alpha)
= (5/13) / (12/13)
= 5/12

Therefore, tan(alpha) = 5/12.