Binomial/Combinatorics Help!

Show that:

(5 C 3) + (5 C 3) = (6 C 3)

Thanks!

(5 C 3) + (5 C 3)
=2*(5!/(2!*3!))
=5!/3!
=(5!/3!)*(6/6)
=6!(3!*3!)
= (6 C 3)

(5 C 3) + (5 C 3) = (6 C 3)

L.H.S. = (5 C 3) + (5 C 3) = 5*4*3 / 3*2*1 + 5*4*3 / 3*2*1

L.H.S. = 10 + 10 = 20 ........................................… [1]

R.H.S. = (6 C 3) = 6*5*4 / 3*2*1 = 20 ................................. [2]

Comparing [1] and [2], we get,

(5 C 3) + (5 C 3) = (6 C 3) >======================< Q . E . D.