I would use embedded data for this. It has worked well for me in the past. Here is a good support article about embedded data. This section in particular deals with how to set values from the survey URL.
Basically, in your Survey Flow, create an embedded data field by clicking "Add a New Element Here" and then selecting "Embedded Data." You can put it at the top of your Survey Flow, and call it something like "Org". When creating your embedded data, be sure to go into "Options" to specify the type - in your case, "Text Set" might work well. There's no need to set a value for the embedded data now; the value will be set in the survey distribution link(s).
When you go to distribute your survey, choose the option to get a single, reusable link. You'll need to take whatever link Qualtrics gives you, and edit it to make 5 different links for each of your organizations. To the very end of each link, you'll add on some text like:

?Org=FirstOrg

where "Org" is the name of the embedded data field you created in your Survey Flow, and "FirstOrg" is the name of the organization that is sending the link (whatever you want it to be called). If you have a LOT of organizations that you need to create links for, then you could put a list of the organization names in Excel and create a formula to fill in the embedded data field for each one.
The support articles I linked to earlier have more details on how to do this. But let us know if you have any issues getting this to work!

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