Search results in specific categories

Depending on which page you enter a search term, I want the search results in different, specific categories.

I’m able to get the ID’s of the categories I want to show. I’m considering to create a custom search url after clicking the search button, like:
http://localhost:8888/wordpress/?s=healthiness&cat=5,2
With this url, only posts are shown in categories with the ID’s 5 and 2.

Do you guys think this is a good idea? And if so, does somebody know how to create a custom search url like this when clicking the search button?

Thanks in advance!