Depending on the type of disaster, you may be able to take a tail-log backup (google or see BoL).

If you can, then your restore would be last full backup, last diff backup, log backups since the diff backup and then the tail log backup for a restore to point of failure.

If you can't, then your restore would be last full backup, last diff backup, log backups since the diff backup ending with the 1pm log backup for 5 minutes of data loss.