Perl4 and perl5 are informal names for different versions of the Perl programming language. It's easier to say "perl5" than it is to say "the 5(.004) release of Perl", but some people have interpreted this to mean there's a language called "perl5", which isn't the case. Perl5 is merely the popular name for the fifth major release (October 1994), while perl4 was the fourth major release (March 1991). There was also a perl1 (in January 1988), a perl2 (June 1988), and a perl3 (October 1989).
The 5.0 release is, essentially, a ground-up rewrite of the original perl source code from releases 1 through 4. It has been modularized, object-oriented, tweaked, trimmed, and optimized until it almost doesn't look like the old code. However, the interface is mostly the same, and compatibility with previous releases is very high. See perltrap/"Perl4 to Perl5 Traps".
To avoid the "what language is perl5?" confusion, some people prefer to simply use "perl" to refer to the latest version of perl and avoid using "perl5" altogether. It's not really that big a deal, though.
See perlhist for a history of Perl revisions.