5-6k/day is not much. That's 1 per 15s on average. Whether you need more RAM or not depends on a variety of things. Most likely you have a peak in traffic sometime during the day. That's what you'll need to look at. How many requests per second are you getting then? What portion are for static items and what portion for scripts (Perl, PHP, etc). If you have a lot of static assets, you can put them on a subdomain under a different user, on a separate domain altogether, behind a CDN (cloudflare, amazon), etc. What scripts/webapp are you running? Some are better at managing memory than others. Some have caching options. How often are you hitting a database? etc, etc, etc.
There's no simple answer that fits everyone. It depends on a lot of different factors. I get 5-10k script requests per day, 99% of which are Ajax requests, and don't have any problems with memory on shared hosting. All of my static assets are on another domain and behind cloudflare with long expires set. All database requests are cached so that, on average, each user may make 100-200 requests, but the database will only be hit a few times.