My problem is, I don't know where to start.

You could start by changing the structure. You now have a hash, whose values are array(ref)s containing strings you have to split. Turn it into a 2 level hash:

{ name1 => {property1 => 8.8016,
            property2 => 4.5016,
            property3 => 4.0873,
            property4 => 7.0726,
            property5 => 9.5121,},
  name2 => { ... },
  name3 => { ... }
};
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You can then easily find your answer (untested):

my $word1 = "...";
my $word2 = "...";
my $data  = { ... }; # Contains the data above
my $sum = 0;
foreach my $property (keys %{$$data {$word1}}) {
    $sum += $$data{$word1}{$property} if exists $$data{$word2}{$proper
+ty};
}
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