There is a bug report regarding files greater that 2Gb on the perl5_porter's mailing list. Apparently it applies to most 64bit systems that have large file support (and that includes Solaris 2.6). You can check it out for yourself.

A snippet from the report says:
... The size returned by lstat is incorrect for files over 2 GB for perl 5.004_04 and earlier versions. I see this under Solaris 2.6 and IRIX 6.2 ...

I would imagine that a likely solution would be to work with perl above 5.004_04, but you already stated that you're working with 5.005_03, so I really don't know what to gather from this.
HTH

#!/home/bbq/bin/perl
# Trust no1!