To find the value of ba x ad, we first need to find the length of segment AD.

Since AD is a bisector of angle BAC, we know that AB = AD.

Now, we can use the Pythagorean theorem to find the length of AD:

AC^2 = AB^2 + BC^2
AC^2 = 5^2 + 12^2
AC^2 = 25 + 144
AC^2 = 169
AC = 13

Since AD = AB = 5, we can now find the value of ba x ad:

ba x ad = 5 x 13
ba x ad = 65

Therefore, the value of ba x ad is 65.