I love that solution. Here it is in the form of a sub. Pass a reference to the hash into the sub. A return value of true means all values are equal. A value of false means there are some not-equal values.

use strict;
use warnings;

my %goodhash = qw/one 1 two 1 three 1 four 1 five 1/;
my %badhash = qw/one 1 two 2 three 2 four 2 five 2/;

foreach my $testhash ( \%goodhash, \%badhash ) {
    print SameVals( $testhash )
           ? "Good.\n" 
           : "Bad.\n";
}

sub SameVals {
    return keys( %{ { reverse %{ $_[0] } } } ) <= 1;
}
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Note that this adds a hashref dereference. That's the  %{ $_[0] } part.