To find the cosine of angle B, we can use the Pythagorean identity sin^2B + cos^2B = 1.

Given sinB = 5/13, we can find cosB as follows:

sin^2B + cos^2B = 1
(5/13)^2 + cos^2B = 1
25/169 + cos^2B = 1
cos^2B = 1 - 25/169
cos^2B = 144/169
cosB = √(144/169)
cosB = 12/13

Therefore, the cosine of angle B is 12/13.