Honestly, I'd recommend that you search CL for the bike you want rather than convert what you have. Those simple conversion projects often end up being not so simple and costing more than in the end than what the bike is worth. With single speeds having a high hipness factor right now, you may even be able to find a used 5 speed for less than what your Bianchi would fetch and make money on the deal.

If you really want to stick with the Bianchi, then your parts list is pretty close. But most likely you will need a new back wheel. If your current hub is a flip flop track style hub, you can't just add a 5 speed cassette to it. You'll either need to find a used wheel, or buy the hub/cassette and have someone rebuild your wheel using the old rim. But by the time you rebuild your wheel you're starting to get into some real money which is why my first recommendation is to find a new (used, but new to you) bike that has the features you want.