ls -l /usr/share | grep perl5
drwxr-xr-x.   49 root root       4096 Mar 31 18:40 perl5
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I don't see how it's a system permissions issue. As user, I can cat the file

made a small test script:

 $ cat perl-test.pl 
#!/usr/bin/perl
use lib '/usr/share/perl5';
use strict;
print "ok";
$ chmod +x perl-test.pl 
$ ./perl-test.pl 
Can't locate lib.pm:   Permission denied at ./perl-test.pl line 2.
BEGIN failed--compilation aborted at ./perl-test.pl line 2.
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Not sure what you mean by printing @INC in a BEGIN block, but I sure don't know how.