Or, you can use Time::Piece (core since 5.10) and Orcish Maneuver:

my %cache;
@sorted = sort {
    ( $cache{$a} //= 'Time::Piece'->strptime($a->{statement_date}, '%m
+/%d/%Y') )
      <=>
    ( $cache{$b} //= 'Time::Piece'->strptime($b->{statement_date}, '%m
+/%d/%Y') )
} @statements;
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