If you are referring to the number of objects that you can store in one Amazon S3 bucket, then it's unlimited.
There is no limit to the number of objects that can be stored in a bucket and no difference in performance whether you use many buckets or just a few. You can store all of your objects in a single bucket, or you can organize them across several buckets.
But if you are talking about the max size of each object then its 5TB
To know more refer to this article.