Idon't understand how to find a. !

I wanted to check that answer so I tried a different approach.
From the Pythagorean Theorem, we know that side b = 13
So, (look at my graphic), we can split up side b into "x" and "13-x"
So, we can say
5^2 = a^2 + x^2     12^2 = a^2 + (13 -x)^2
25 - x^2 = a^2        a^2 = -25 + 26x -x^2
Therefore,
25 - x^2 = -25 + 26x -x^2
26x = 50
 x = 1.9230769231
If x = 1.9230769231 then
a^2 = 5^2 -1.9230769231^2
a^2 = 25 -3.6982248521
a^2 = 21.3017751479
a = 4.6153846154