Limit number of posts user can read?

I’ve tried searching for this but it only seems to bring up methods of limiting posts a user can make or restricting categories.

I want a system whereby a registered user on the site can browse a certain number of articles in a given time (say per day/week/month) and then when they’ve looked at, for instance, five posts, their access to all other post on the site becomes restricted.

I’m imagining something using cookies would do this but I wanted to see if there was anything within WordPress that would work (as that’s what the site in question will be built using) as it will also need to link to WordPress user types (ie one type of user can browse 5, another 10, etc, so users are insentivised to upgrade their membership and see more content).

Thanks in advance for any help offered.