Hi
as baltwo says - Safari 5
is available for Leopard, and the fact that it installed at all, shows that you
did use the Leopard version of the install package, since the Snow Leopard version checks made before any files are written, to see that you're not running anything except OS X 10.6.x.
That said, it's very likely you have some add-on or plugin which conflicts badly with Safari 5.
You can see Apple's advice on that Unsupported third-party add-ons may cause Safari to unexpectedly quit or have performance issues
and also perhaps locate the Crash Report that
may have been added to Home/Library/Logs/CrashReporter/ when Safari wouldn't launch...
it'll be named something like
Safari
2010-06-06-002302_your_computername.crash
where the date is the most recent one you see.