You can't generate 5000 thumbnails at once for sure with a shared account. It will be too much.
The best would be to generate them on your computer and upload them I know I can do that with other scripts than gallery2.
Otherwise you will have to generate thumbnails by group. I mean 20 by 20 for example.
Ok maybe better if you can't do the first solution, install all locally on your computer with easyphp, generate the thumbnails and then upload all on your real server.

Hello,

 I personally do not have an opinion on which is better; But we provide PHP GD, and ImageMagick. I am not 100% sure, but I do not think we offer NetBPM at this time.

 As for the thumbnail questions; dart is correct. You should be able to do this on the shared plan as long as you upload them in batches for thumbnail production, or if you generate the thumbnails on your local machine then upload them.

I hope this helps!
-Derek