How can I move s3 objects >5gb from one bucket to another?

Currently, what you're trying to do can't be done in a single operation. Move in S3cmd to the API is essentially a copy and delete all in one and it's a restriction of the copy operation.

http://docs.aws.amazon.com/AmazonS3/latest/API/RESTObjectCOPY.html

You can store individual objects of up to 5 TB in Amazon S3. You create a copy of your object up to 5 GB in size in a single atomic operation using this API. However, for copying an object greater than 5 GB, you must use the multipart upload Upload Part - Copy API

http://docs.aws.amazon.com/AmazonS3/latest/dev/CopyingObjctsMPUapi.html

The examples in this section show you how to copy objects greater than 5 GB using the multipart upload API. You can copy objects less than 5 GB in a single operation.