I have been taught since 4th grade that Pensacola, Florida was settled
in 1559, five years before St. Augustine. After St. Augustine was
settled, a hurricane wiped out the settlement at Pensacola. The
survivors returned later and relocated Pensacola to Santa Rosa Island.
That is why St. Augustine is always referred to as the oldest
PERMANENT settlement in North America. Correct?

I think the better way to phrase it would be "the oldest continuously
inhabited European settlement in North America" if one is a stickler.

MSN's Encarta has the following article.
http://encarta.msn.com/encyclopedia_761570777_7/Native_Americans_of_North_America.html

"The Acoma Pueblo, located atop a mesa in west central New Mexico and
founded in AD 1075, is believed to be the oldest continuously occupied
settlement in the United States."

What about the Viking settlement in L'Anse aux Meadows, Newfoundland?
It dates from about 1000, so it should qualify as the oldest European
settlement in North America.

Scriptor

I agree that one could refer to St. Augustine as the oldest
continuously occupied settlement. The ones earlier were not
continuously occupied.

1559 is the date that the settlement by Don Tristan De Luna was
founded, but to correct your location of it, it was on Santa Rosa
Island. It was, as you stated, pretty well destroyed by the Hurricane,
altho I am not sure if it was before, or after, the settlement at St.
Augustine had been established. The re-settlement was made on the
north shore of Pensacola Bay because of the havoc that the first
settlement endured from the Hurricane at it's location on the island.
As for whether it was the first European settlement or not, I suppose
the Vikings can lay claim to being the first, but Pensacola was
certainly the first Spanish settlement, as De Luna was a Spaniard.