If you plan on taking the test, then yes, you should do the N5 mastery schedules. If you don't, then it's up to you to weigh the pros and cons.
You say every word you use isn't one you've studied, but one you had to look up. What do you mean by use? Words you read or that you say? In what context? Are you speaking with other people? Reading manga? Watching YouTube?
Regardless, it's kinda normal in the beginning. The basics words are just that, basic. They're words that cover normal everyday concepts. If you're using Japanese to watch anime, not to talk about washing the dishes, then of course you're not using your Renshuu vocab. But even if all you do is watch anime, you'll need these words eventually.
Some people prefer to avoid Renshuu's lessons and mine vocab from real world sources, like books and TV. They get more enjoyment from that process. I don't enjoy this method at my current level, so I avoid it.
If you plan on taking the lower levels of the JLPT, you're better off following Renshuu's curriculum. It'll teach you everything you need for the test. But you might feel like the Japanese you learn isn't useful for you. It IS, but you might not realize it for a while.
If you use Renshuu's grammar cards, you're also better off following Renshuu's curriculum. The grammar cards expect you to know certain vocab words. If you do N5 vocab and N5 grammar, you'll know all the vocab you need for the grammar cards. If you pick and choose vocab and grammar yourself, you'll have grammar lessons with words you don't know yet.
