From the way you describe it, you have each user making their own requests and caching client-side only. When I mentioned duplicate streamers I mean multiple end users all wanting data about the same streamer.
For example, if I was to use your app and also wanted data on Monstercat, GRONKH, and SoftCreatR, it would be redundant for me to make requests to Twitch for that data if you (and however many other users might want that data too) if there’s already someone else requesting it.
If you were to use a server-side cache, you could have an unlimited number of end users all want to see data on Monstercat, but it only ever be 1 request to each of the required endpoints every 5 min, as users would just use the same cache. Being a single point of making requests too means that you could use a single app token with 1,000/min rate limit, or higher, which would account for your needed usage, as well as not requiring every single end user having to get and enter their credentials into your app.