If it's a one off job Id say illustrator isn't worth it. Setting up that many variables for 5 sheets...
But if it's an ongoing thing, use Illy. The initial setup of hundreds of variables may take you an Hour or two...but importing the csv file and exporting to pdf or.eps will take minutes, if not seconds for this and all future jobs.
I know you want to learn it yourself. But if you post your illustrator file you already have, it won't take long to create your template... Then you use your template yourself to import your Excell files.
It's super easy.... But tbh, learning to do it from scratch is 100x harder than taking someone's already setup file, see how it's setup and understanding it from there and using that file to learn how to make your own.
We do license plates this way. In our province off road vehicles need reflectice decals - we do 10,000 every 3 months - spent an hour to setup the file... Then the excel file takes us a minute to modify every 3 months, and it takes 5 minutes to export 900 ft of vinyl printing.
For some one off stuff Indesign might be better. But if it's the same design/layout and just the data is variable... Illustrator works perfectly.
I highly suggest posting, or messaging the excel data + your illustrator layout here... With all the scripts i use for variable naming/importing it'd take 5 mins to do a template setup for you... Then you can dissect it and see how it's built and tweak it. Or use it to start from scratch to optomize your setup. That way you can see if it works the way you like before fully learning how to do it yourself.
Much better than banging your head against the wall going from software to software.... There's been what, 5 recommendations on here so far on what to use? Use what you know and ate comfortable with, which seems to be Illy!
[Edit] or if you'd like,I can send you our license plate file (with the graphics removed), you can see.how it's setup and use the same concept for your file. We have a cnc version with fiducials and everything...should be similar to your setup.