SET @a:=10;
UPDATE 
    table
SET
    table.ID=@a:=@a+1
WHERE
    table.ID=5
[download]

In sqlite I employ limit

#!/usr/bin/perl --
use strict;
use warnings;
use DBI;
use DBD::SQLite;
use Data::Dump qw/ dd /;

unlink 'goner.sqlite';

my $dbh =  DBI->connect(
    "DBI:SQLite:database=goner.sqlite",
    undef, undef,
    {qw/RaiseError 1/}
);
eval {
    $dbh->do('CREATE TABLE NameId ( ID INTEGER , Name TEXT );');
    $dbh->do(q!INSERT INTO NameID ( ID, Name ) VALUES ('1','bar');!);
    $dbh->do(q!INSERT INTO NameID ( ID, Name ) VALUES ('2','bar');!);
    $dbh->do(q!INSERT INTO NameID ( ID, Name ) VALUES ('5','FEE');!);
    $dbh->do(q!INSERT INTO NameID ( ID, Name ) VALUES ('5','FII');!);
    $dbh->do(q!INSERT INTO NameID ( ID, Name ) VALUES ('5','FOO');!);
} or warn "$@";


dd( $dbh->selectall_arrayref('select * from  NameID' ) );
dd( $dbh->selectrow_array(q{ select COUNT(*) from  NameID WHERE ID='5'
+ } ) );


#~ http://www.sqlite.org/compile.html#enable_update_delete_limit
#~ https://www.sqlite.org/lang_update.html
#~ https://dev.mysql.com/doc/refman/5.0/en/update.html
my $sql = qq{
UPDATE
    NameID
SET
    ID=?
WHERE
    ID='5'
LIMIT
    1
};

my( $count ) = $dbh->selectrow_array(q{ select COUNT(*) from  NameID W
+HERE ID='5' } );
my $nid = 10;
while( $count ){
    dd({ rowsaffected => $dbh->do( $sql, {}, $nid ) });
    dd( $dbh->selectall_arrayref('select * from  NameID' ) );
    $nid++;
    $count--;
}
undef $dbh;
unlink 'goner.sqlite';
__END__
[[1, "bar"], [2, "bar"], [5, "FEE"], [5, "FII"], [5, "FOO"]]
3
{ rowsaffected => 1 }
[[1, "bar"], [2, "bar"], [10, "FEE"], [5, "FII"], [5, "FOO"]]
{ rowsaffected => 1 }
[[1, "bar"], [2, "bar"], [10, "FEE"], [11, "FII"], [5, "FOO"]]
{ rowsaffected => 1 }
[[1, "bar"], [2, "bar"], [10, "FEE"], [11, "FII"], [12, "FOO"]]
[download]