How can I move a MySQL database from 5.1 to 5.6? I have pretty big database, like with 5 000 000 rows in total. It is located in a remote server. I want to copy this database to my personal computer, for testing purposes. However I don't know the best option for this operation. Dumping the database does not look user friendly. Can I use Navicat's data transfer function to do this? Could it end with error? I think this operation can last few hours. Is there any other ways?
It's all here. What's wrong with 

mysqldump options | mysql localhost_name -u me -pmy_password


(with valid options for your particular setup)? Check here for a sample. I don't know for sure, but Navicat is, in all likelihood doing something similar in the background. This is possibly better.