Your match (.+) is greedy so it will match as much as possible, i.e. up to the second </year>. Make it non-greedy with the addition of a question mark.

$ perl -E '
> $var = q{<x><year>2010<day>5</day></year><month>January</month> <day
+>31</day>, <year>2010</year></x>};
> say $1 if $var =~m{<year>(.+?)</year>};'
2010<day>5</day>
$
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I hope this is helpful.