Use the following three identities to evaluate the given integrals.

sin mx sin nx = 1/2 (cos ((m - n)x) - cos (m + n)x))

sin mx cos nx = 1/2 (sin ((m - n)x) + sin ((m + n)x))

cos mx cos nx = 1/2 (cos ((m - n)x) + cos ((m + n)x))

∫ sin 5x sin 7x dx