The short: Yes any creature that suffers leathal damage 'dies' including those with Defender.
A wall as they were previously known, is a creature with defender.
If it takes 5 damage it is destroyed.(Dies)
Rule 119 all parts but this one in particular:
119.5. Damage dealt to a creature or planeswalker doesn't destroy it. Likewise, the source of that damage doesn't destroy it. Rather,
state-based actions may destroy a creature or planeswalker, or
otherwise put it into its owner's graveyard, due to the results of the
damage dealt to that permanent. See rule 704.
And the state based action is what sends the creature to the grave yard:
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.
702.3a Defender is a static ability.
702.3b A creature with defender can't attack.
702.3c Multiple instances of defender on the same creature are redundant.
So a 'Defender' is simply a creature with an ability. Any creature that has damage marked on it that is greater than it's toughness, is destroyed as a state based action.