AWS S3 documentation says:
Individual Amazon S3 objects can range in size from a minimum of 0 bytes to a maximum of 5 terabytes. The largest object that can be uploaded in a single PUT is 5 gigabytes.
How do I store a file of size 5TB if I can only upload a file of size 5GB?
According to the documentation here you should use multipart uploads:
Upload objects in parts—Using the multipart upload API, you can upload large objects, up to 5 TB.
The multipart upload API is designed to improve the upload experience for larger objects. You can upload objects in parts. These object parts can be uploaded independently, in any order, and in parallel. You can use a multipart upload for objects from 5 MB to 5 TB in size.
Here there is a list of the APIs and an example on how to use each one.