Most casinos allow you to split two initial cards of the same value and play them as two separate hands while staking an equal amount to the first bet on the new hand.
You never split two 5s or two 10s. If you have two 5s you have a total of ten and a very good chance of drawing a ten to make a strong hand of 20. If you have two 10s you are already there.
However, if you have two Aces or 8s you should usually split them. The two aces give you two chances for Blackjack, (although it generally only pays evens on split hands) and two 8s gives you two chances to make 18 instead of the rather poor 16 that you have.
The other splitting decisions depend more on the dealer’s face up card and you need to consult the full Blackjack Strategy section for more information.