Imagine a line running down the middle of Florida (roughly, not exactly).

If an aircraft flies north or south along this line, and is approximately
5 miles in the air, can the pilot see both coasts (the Gulf of Mexico
in the west, AND the Atlantic Ocean in the east) with the naked eye
or with high-quality binoculars?

I guess another way of asking this question is, if one is 5 miles in the air,
how far can one see?

Assume that there are no buildings or trees to block the view.

You might find this prior thread of interest:
http://answers.google.com/answers/threadview?id=420365

On my map of the US, it looks like Florida is less than 150 miles
wide. From the middle of Florida, the west coast and the east coast
are both 75 miles away.

According to thread 420365, at 5 miles in the air, we can see 214.5
miles (if my calculations are correct).

So, if you're 5 miles in the air over Florida and you look west,
you'll see 75 miles of land and 139 miles of water (Gulf of Mexico). 
Same thing if you look east.

Wow, I'm surprised.  I would have bet my salary that you wouldn't be
able to see either coast!

I'm guessing it would matter how clear of a day it is.  Also how much
water vapor and other particles are in the air.  Example when you look
at a moutain or hill that may only be a mile away it looks lighter or
gray/bluish in color. Air itself tends to defract colors. Thats why
the have visability distances in wheather forcasts.  So I'm guessing
that you cannot see 75 miles away it would look blue like the sky.