Yes, that would work in this case, but in general, is there a correct way to perform this abstraction?

What if I want to find the value to $$x, where $x is the name of the scaler variable I am interested in?

Re-reading what you say you want, this seems to meet all your requirements:

my (@a, @b, @c, @d); # create and populate arrays

#Define a "Mapping hash":
my %aref = (a=>@\a,  b=>\@b,  c=>\@c,  d=>\@d  );
 # (Same as toolc's solution)
my $x = "b"; # I want to access "@b"

my $extracted_value_5_from_b = $aref{ $x }->[5];
my @entire_array_b_copy = @{ $aref{ $x } };

# Alternative, closer to the syntax you seek..
my $y = $aref{ b };

for ( @$y ){
  # We are iterating through @b here ...
}

#-- Strict-compliant, maintainable version ...
my $z=\@b;
for ( @$z ){
  # We are iterating through @b here ...
}
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     Syntactic sugar causes cancer of the semicolon.        --Alan Perlis

Do you mean something like this ?

perl -e "my (@a,@b,$x); @a=0..5;@b=20..25; for $x(\@a,\@b){print qq|@$
+x;\n|}"
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Prints:
0 1 2 3 4 5;
20 21 22 23 24 25;

     Syntactic sugar causes cancer of the semicolon.        --Alan Perlis