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 (232−1232−1 bytes). Video applications, large databases, and some other software easily exceed this limit. Larger files require another formatting type such as NTFS.
Or you could split the zip file in two 3.5 GB parts.