Select highest id of each type in mysql
I think you're looking at something like this:

Select A.Max_id, 
harddrives.id As id1,
  harddrives.serial_number,
  brands.name,
  harddrives.size,
  location.name As name1,
  encryption_type.name As name2,
  resource.name As name3,
  backups.start_time,
  backups.end_time
  FROM  
  ( Select  backups.resource_id,
    Max(backups.id) As Max_id
      FROM backups  Group by backups.resource_id 
      Order By backups.start_time Desc ) A 
JOIN resource ON resource.id = A.resource_id Inner Join
  harddrives On backups.backup_drive_id = harddrives.id Inner Join
  brands On harddrives.brand_id = brands.id Inner Join
  location On harddrives.location_id = location.id Inner Join
  encryption_type On harddrives.encryption_type_id = encryption_type.id

OR (order by outside, don't remember)

Select A.Max_id, 
harddrives.id As id1,
  harddrives.serial_number,
  brands.name,
  harddrives.size,
  location.name As name1,
  encryption_type.name As name2,
  resource.name As name3,
  backups.start_time,
  backups.end_time
  FROM 
  (  Select  backups.resource_id,
    Max(backups.id) As Max_id
  FROM backups  Group by backups.resource_id ) as A 
JOIN resource ON resource.id = A.resource_id Inner Join
  harddrives On backups.backup_drive_id = harddrives.id Inner Join
  brands On harddrives.brand_id = brands.id Inner Join
  location On harddrives.location_id = location.id Inner Join
  encryption_type On harddrives.encryption_type_id = encryption_type.id
Order By   A.start_time Desc