Why can't I copy a 5G file?

/media/LACIE sounds like you're handling a pre-formatted drive, most likely with the FAT32 filesystem. According to Wikipedia, the maximum file size for FAT32 is about 4GB.

I suggest to reformat the drive to either ext4 (for supporting Linux file permissions) or NTFS (if you need to share the drive with windows users).

How funny, but you've now to backup your backup first before reformatting ;)

If you need to keep the fat32 filesytem there is a way around the limit.

There is a command called split that will let you split an archive into smaller parts.

 -b, --bytes=SIZE
              put SIZE bytes per output file

Example:

dd if=/dev/zero bs=1M count=150 >test

150+0 records in
150+0 records out
157286400 bytes (157 MB) copied, 0.439344 s, 358 MB/s

split test -b 10000000

ls -l
 157286400 2011-06-01 21:18 test
  10000000 2011-06-01 21:20 xaa
  10000000 2011-06-01 21:20 xab
  10000000 2011-06-01 21:20 xac
  10000000 2011-06-01 21:20 xad
  10000000 2011-06-01 21:20 xae
  10000000 2011-06-01 21:20 xaf
  10000000 2011-06-01 21:20 xag
  10000000 2011-06-01 21:20 xah
  10000000 2011-06-01 21:20 xai
  10000000 2011-06-01 21:20 xaj
  10000000 2011-06-01 21:20 xak
  10000000 2011-06-01 21:20 xal
  10000000 2011-06-01 21:20 xam
  10000000 2011-06-01 21:20 xan
  10000000 2011-06-01 21:20 xao
   7286400 2011-06-01 21:20 xap

Oh and cat puts them back together.