Easy peasy!
As long as you also have an id in your entries table, this is the SQL query you need to run:
Code:
int updateCount = entityManager.createNativeQuery(
   "update entries set c5 = 1 " +
   "where id in " +
   "( " +
   "    select id " +
   "    from ( " +
   "        select *, MAX (c3) OVER (PARTITION BY c1, c2) as max_c3 " +
   "        from entries " +
   "    ) t " +
   "    where t.c3 = t.max_c3 " +
   ") ")
.executeUpdate();
If the database does not support Windows Functions, then the query looks like this:
Code:
int updateCount = entityManager.createNativeQuery(
   "update entries set c5 = 1 " +
   "where id in " +
   "( " +
   "    select e.id " +
   "    from entries e  " +
   "    inner join ( " +
   "        select c1, c2, max(c3) as max_c3 " +
   "        from entries " +
   "        group by c1, c2 " +
   "    ) t " +
   "    on e.c1 = t.c1 and e.c2 = t.c2 and e.c3 = t.max_c3  " +
   ") " )
.executeUpdate();
Check out 
this article for more details.