UTF-16LE is supported by the Encoding module, so it should work... Did you try down converting it to Latin-1? The less often used encodings don't have as many aliases, you may need to be more careful about how the encoding is specified.

Encode::from_to($string, 'UTF-16LE', 'utf8');
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should be ok, as should

Encode::from_to($string, 'UTF-16LE', 'iso-8859-1');
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You only need to single escape the forward slash in the regex. (Or use alternate delimiters.)

my $string = '5/18/05  184  7    3.8%    6.14    1.13';

if ($string =~ m#(\p{Digit}+/\p{Digit}+/\p{Digit}+)#){
    print $1;
}
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