what is the safest, fast [ 0 to 60 in around 5 seconds], 4 seat,
convertible sports car

Hello 68chief-ga

In the light of no formal safety crash test results, it 'might' be
something German, who normally take safety quite seriously with
performance to match. A BMW M3 convertible 'might' be quite safe if
based on the saloon Euro NCAP ratings, (
http://www.euroncap.com/ratings.php3?id=large_family_cars&order=1 )
though it is important to point out in topless form without the extra
rigidity of the car shell, C pillar airbags, overhead curtains and
other factors, it will perform very differently in crash tests, so
it's only an assumption. There appears to be no independent crash
tests on it or other high performance sports cars particularly in
convertible form as most crash testing focuses on testing mainstream
high volume sales cars. (for greater benefit to the public)
Euro NCAP
http://www.euroncap.com/results.htm 
NHTSA
http://www.nhtsa.dot.gov/NCAP/Search.cfm
OSA
http://www.osa.go.jp/anzen/html2002e/as106.html
MYNMA
http://www.mynrma.com.au/motoring/cars/crash_tests/ancap/index.shtml

Actually, there are not that many 4 seater convertible cars which can
accelerate to 60mph in around 5 seconds for consideration.
Convertibles are heavier than their closed top counterparts so their
0-60 times are jaded taking them into the 6 seconds territory, e.g.
Mercedes CLK 55 AMG does 6.1 seconds (
http://www.supercars.net/cars/2002@$Mercedes-Benz@$CLK%2055%20AMG%20Cabrioletg.html
 ) and the majority of sports cars in this convertible category are 2
seaters or 2+2 seaters - the rear only suitable for a small child.

The BMW M3 convertible does 0-60 in around 5.4 seconds
Edmunds.com "Road Test Follow Up: 2002 BMW M3 Convertible" by Karl
Brauer
http://www.edmunds.com/reviews/roadtests/spin/71189/article.html

The Volvo C70 T5 convertible has 4 seats, a 240 horse power engine,
but 'only' does the 0-60 sprint in a slow 7.5-8.0 seconds.
SuperCars.net
http://www.supercars.net/garages/Moonracer/70v2.html

Another car which 'might' be around the 5 second mark is the Pontiac
Firebird Trans AM convertible, but again there is no safety test data.
http://www.supercars.net/cars/2002@$Pontiac@$Firebird%20Trans%20Am%20Convertibleg.html

Search Strategy:
SuperCars.net
http://www.supercars.net/index-sixty.html
http://www.supercars.net/index-present.html
What Car? Buyers Guide - What Car? magazine, Haymarket Motoring
Publications Ltd.
MSN Carpoint
http://carpoint.msn.com

I hope that helps, if you need any clarification of the answer just
ask.
Kind regards
lot-ga

Dear 68chief,

I researched this 3 years ago and the answer was Volvo.  Here is why. 
First, 4 real adults can fit in the car - it has a real back seat. 
Second, it is REALLY safe (I don't have time to tell you why here - go
read).  Third, if you order one made to your specs (this is fairly
common as the dealer may not have what you want on the lot), you can
have them put a bigger engine in for you.  It's not huge (I think 240
hp), but the car can go like a bat out of hell.  Forth, it has a real
trunk.  The features on this car are superb.  I ordered one 3 years
ago.  Good luck on your search.

JCG