Your opponents Grizzly Bear will survive. Damage is dealt simultaneously but because the lethal damage is checked as state based action it will not happen until after your opponent has 5 life and the Fateful hour ability has kicked in.
510.2. Second, all combat damage that's been assigned is dealt simultaneously. This turn-based action doesn't use the stack. No
player has the chance to cast spells or activate abilities between the
time combat damage is assigned and the time it's dealt. This is a
change from previous rules. Example: Squadron Hawk (a 1/1 creature
with flying) and Goblin Piker (a 2/1 creature) are attacking. Mogg
Fanatic (a 1/1 creature with the ability "Sacrifice Mogg Fanatic: Mogg
Fanatic deals 1 damage to target creature or player) blocks the Goblin
Piker. The defending player sacrifices Mogg Fanatic during the declare
blockers step to deal 1 damage to the Squadron Hawk. The Hawk is
destroyed. The Piker deals and is dealt no combat damage this turn. If
the defending player instead left Mogg Fanatic on the battlefield, the
Fanatic and the Piker would have dealt lethal damage to one another,
but the Squadron Hawk couldn't have been dealt damage.\
510.4. Fourth, the active player gets priority. Players may cast spells and activate abilities.
704 State-Based Actions
704.1. State-based actions are game actions that happen automatically whenever certain conditions (listed below) are met. State-based
actions don't use the stack.
704.3. Whenever a player would get priority (see rule 116, "Timing and Priority"), the game checks for any of the listed conditions for
state-based actions, then performs all applicable state-based actions
simultaneously as a single event. If any state-based actions are
performed as a result of a check, the check is repeated; otherwise all
triggered abilities that are waiting to be put on the stack are put on
the stack, then the check is repeated. Once no more state-based
actions have been performed as the result of a check and no triggered
abilities are waiting to be put on the stack, the appropriate player
gets priority. This process also occurs during the cleanup step (see
rule 514), except that if no state-based actions are performed as the
result of the step's first check and no triggered abilities are
waiting to be put on the stack, then no player gets priority and the
704.5g If a creature has toughness greater than 0, and the total damage marked on it is greater than or equal to its toughness, that
creature has been dealt lethal damage and is destroyed. Regeneration
can replace this event.