What happens when a 5/5 blocks a 6/4?
Unless one of those creatures has First Strike or Double Strike, they will deal combat damage simultaneously. The following will happen:


Your 6/4 will deal 6 damage to your opponent's 5/5. (Note that 6 &ge; 5.)
At the same time, your opponent's 5/5 will deal 5 damage to your 6/4. (Note that 5 &ge; 4.)
State based actions kick in, see that both creatures have damage greater than or equal to their toughness, and both creatures die.