To be honest Perl 5 isn't really like Perl 4. They are quite different languages - Perl 4 didn't have objects, and Perl 5 places heavy emphasis on them.
Up to you to decide when you think it started, but I'd say the current language we think of as "Perl" started with the release of Perl 5.
Most Perl 4 runs under Perl 5, and most Perl 5 written in the early years did not place heavy emphasis on objects. When I started in Perl, it was common to write code in such a way that it would run under either because it might have to.
Today, objects are used heavily. And furthermore the way we write those classes has changed a lot since Moose and friends became popular. As a result most Perl code bases written in the last dozen years look less like early Perl 5 than early Perl 5 looked like Perl 4.
Perl 4 and Perl 5 are more of a continuum than different languages.
Python 1.2 was released in 1995.
The first public release of Java as 1.0 was in 1996.
JavaScript appeared in 1995 as well, but the first ECMAScript standard didn't appear until 1997.
First release of PHP was in 1995, same with Ruby.
Perl pre-dates the initial release of all those languages and was already up to its fifth major version by that time.