Note that when the string includes mixed quoting which is not valid in the OP's terms:

my $string = qq{var1='1' var2="2" var3="3" var4='4" var5="5' var6="correct"};

...hipowls non-5.10 version (5.10 not tested) produces "ugly" output in the sense used by almut and skeeve

var1 = 1
var2 = 2
var3 = 3
var4 = 4" var5="5
var6 = correct
[download]

More significantly, if $str is in the form:

my $string = qq{var1='1' var2="2" var3="3" var4='4" var5="5'

...the output becomes:

var1 = 1
var2 = 2
var3 = 3
var4 = 4" var5=
[download]

...which is the same as the output produced if var5 is properly quoted, var5='5':

my $string = qq{var1='1' var2="2" var3="3" var4='4" var5='5'};

i.e.,

var1 = 1
var2 = 2
var3 = 3
var4 = 4" var5=
[download]

That sort of ambiguity may be a problem for OP.