These machines are a hot mess in terms of what works and doesn't. Some of them use an IDE ZIF (1.8”) drive which is nearly impossible to find short of gutting an older iPod or Zune, basically. The other ones use a 2.5” drive, but it has to be I/II/III compatible - SATA III Fixed speed drives will not work. What capacity is the original drive? That may be a clue. In addition, check Device Manager for a drive model to tell as well.
If you are lucky enough to have a 2.5" system, you can install just about any drive under 2TB you want - as long as the right SATA support is there. As a general rule, with the ZG5 if it came with an SSD, it's usually IDE. TYPICALLY, this drive is difficult to find (and if you do, it often costs more than the netbook is worth). The IDE drives are just not worth upgrading due to cost :(.
The problem is you need to do a complete teardown to see which board you have. The ZG5 doesn’t have access panels on it for easy HD/RAM access. The guide can be found here.