At first glance I would say:

#!/usr/bin/perl -w
use strict;


my %hash = ('1' => 'cat',
'3'=> 'mouse',
'5'=>'whale'
);

my $elem = 2;

if (defined($hash{2})) {print $hash{2}} 
else {
print $hash{$elem+1}};

1;
[download]

But at second glance I realize that $elem+1 may not exist either in which case you should just failout like so:

#!/usr/bin/perl -w
use strict;


my %hash = ('1' => 'cat',
'3'=> 'mouse',
'5'=>'whale'
);

my $elem = 2;

if (defined($hash{$elem})) {
   print $hash{$elem} } 
elsif (defined $hash{$elem + 1} )
  {
  print $hash{$elem+1}
 }
else {
  print 'ERROR!!!!!!';
} 

1;
[download]