How long will it take to migrate a 5 GB Database to Amazon RDS
The usual answer: It depends

I'm assuming that you've read this guide on how to import data into an Oracle RDS (I chose Oracle because it's what I know, and you don't say what instance type you're using): http://docs.aws.amazon.com/AmazonRDS/latest/UserGuide/Oracle.Procedural.Importing.html

There's similar guides for MySQL: http://docs.aws.amazon.com/AmazonRDS/latest/UserGuide/MySQL.Procedural.Importing.NonRDSRepl.html

Have a look at the guides and do some tests, they should provide you with some idea of timescales.