Maybe your External HDD is formatted as FAT? FAT-formatted drives can't see files larger than 4 GB, you'll have to reformat it as NTFS.

> The maximum possible size for a file on a FAT32 volume is 4 GB minus 1 byte (2<sup>32</sup>−1 bytes). Video applications, large databases, and some other software easily exceed this limit. Larger files require another formatting type such as NTFS.

[FAT32 @ Wikipedia][1]


  [1]: http://en.wikipedia.org/wiki/Fat32#FAT32

Or you could split the zip file in two 3.5 GB parts.