1. I've put it on subreddits but haven't got the traction I wanted. I think the product might not be solving the correct problem. Hence, I didn't try to cold message people with it.
2. The price point is 5$/month which really not feasible to contact customers individually. If I do 100 cold outreaches a day, 10 try the product and one converts, it's 5$/day salary.
i think that is your problem there. The product is too cheap. How much value do you think a customer could get if it were successful at selling?
Go back to the classic YC advice, do things that are not scalable. Cold call a few a day and use it as a way to get users and feedback. It will also give you more users, some of which may have networks that they may share it with.