Try this array* formula:
=SUM(IF((A1:A100=5)*(B1:B100=10),C1:C100))
*As this is an array formula, then once you have typed it in (or
subsequently edit it) you must use CTRL-SHIFT-ENTER (CSE) rather than
just ENTER. If you do this correctly, then Excel will wrap curly braces
{ } around the formula when viewed in the formula bar - you must not
type these yourself.
Hope this helps.
Pete