50k categories and 500k products?

Not sure on the categories, but I have a client with about 225K products with a price matrix that is over a million rows and it seems to perform just fine. Of course your mileage will vary depending on mysql config, disk sub-system, other underlying hardware, etc.

That's an awful lot of categories though. Certainly couldn't display them and since I believe they are cached, you might get some concurrency issues related to reading in the cache for every page load. I'd get an extra few GB of memory and use the SHMEM caching model for that case.

if i have 3k categories and 10 lanauges service.

fact on db table 30,000 categories.

it means 30,000 categories can not be fast. i 'v been try to solve speed isuue for 6 month

i have 5k categories and 10 lanauges. and 100k product list. but always headace for speed of loading.