Grabbing data from a query with specific criteria, then the data around it
First a query without rank. You may get more than 11 rows in the result, if there people with same number of Kills as your player:

  ( SELECT a.*
    FROM AgStats AS a 
      JOIN 
      ( SELECT Kills  FROM AgStats 
        WHERE Name = 'VoidWhisperer'
          LIMIT 1 
      ) AS k
      ON a.Kills &gt; k.Kills
    ORDER BY a.Kills ASC
      LIMIT 5
  )
  UNION ALL
  ( SELECT a.*
    FROM AgStats AS a 
      JOIN 
      ( SELECT Kills  FROM AgStats 
        WHERE Name = 'VoidWhisperer'
          LIMIT 1 
      ) AS k
      ON a.Kills = k.Kills
  )
  UNION ALL
  ( SELECT a.*
    FROM AgStats AS a 
      JOIN 
      ( SELECT Kills  FROM AgStats 
        WHERE Name = 'VoidWhisperer'
          LIMIT 1 
      ) AS k
      ON a.Kills &lt; k.Kills
    ORDER BY a.Kills DESC
      LIMIT 5
  ) 
ORDER BY Kills DESC ;




This will show no more than 11 rows, even if there hundreds of players with same number of Kills, by applying an order on the two columns: Kills, Name:

  ( SELECT a.*
    FROM AgStats AS a 
      JOIN 
      ( SELECT Kills, Name  FROM AgStats 
        WHERE Name = 'VoidWhisperer'
          LIMIT 1 
      ) AS k
      ON a.Kills = k.Kills AND a.Name &gt; k.Name
      OR a.Kills &gt; k.Kills
    ORDER BY a.Kills ASC, a.Name ASC
      LIMIT 5
  )
  UNION ALL
  ( SELECT a.*
    FROM AgStats AS a 
    WHERE Name = 'VoidWhisperer'
  )
  UNION ALL
  ( SELECT a.*
    FROM AgStats AS a 
      JOIN 
      ( SELECT Kills, Name  FROM AgStats 
        WHERE Name = 'VoidWhisperer'
          LIMIT 1 
      ) AS k
      ON a.Kills = k.Kills AND a.Name &lt; k.Name
      OR a.Kills &lt; k.Kills
    ORDER BY a.Kills DESC, a.Name DESC
      LIMIT 5
  ) 
ORDER BY Kills DESC, Name DESC ;


It will be good if you have a an index on (Kills, Name) and a (unique) index on (Name).

Tested at SQL-Fiddle