What you need to do is find out if you could get a different graphics card in the SAME model of your Sony besides the Intel HD GMA.
If they made a motherboard with a Nvidia or AMD GPU that would fit into your SAME chasss, you can find that motherboard, buy it, install it, and hopefully boot up into a new GPU situation.
1. its expensive... honestly, you have a first gen i3, and this upgrade could cost you at LEAST $200 in the US, as you would have to get the motherboard AND compatible heatsink cooler to fit the new motherboard.
That i3 is pushing 4 years old now, and its really not worth investing that much money into
2. I don't think Sony optioned your laptop with any other GPUs. It could be that I don't understand how to read Vaio part numbers, but I can't find the same laptop body with any other GPU available.
3. Its REALLY hard to find a company that actually sells motherboards for laptops, and if you can they usually don't show accurate pictures or list what GPU is on it because they don't know. they just pull from a working laptop and use stock images that don't say what MB you are getting.
the best way to find out is to search for heatsinks that fit your model Sony and see if they have more than a couple variations, and that will tell you if there is one available that will cover the CPU and an additional onboard GPU...
but there's no guarantee that someone selling a MB will list if it has a GPU on it.
I wonder what happen if you install 13.1(1/17/2013) drivers for a desktop HD 5470...dunno if it will let you install, else you are stuck with 2010 drivers i guess.
I've learned it's best to use the drivers from the manufactures website, even if they are ANCIENT because they have the built in power saving functions and sleep mode functionality that AMD doesn't build into their drivers.
From my experience, using AMD's drivers for mobility on Dell's and Acer's has resulted in my laptops not being able to wake up from sleep and losing the ability to do things like dim the screen using the Power Settings feature as well as go correctly into power saving mode.
Changing the motherboard would be too much hassle for an inexperienced hand not to mention that what can fit in there probably won't be very different from what he already has.
Good info about the desktop driver, OP would be better getting a new system if the actual one doesn't suffice him.
Mid range laptops have the graphics chip soldered to the main motherboard in most cases.
So an option to upgrade it will not exist. FYI Gaming laptops for example come with a Mini Pci-E slot on the laptop motherboard this allows you like in a tower system to remove the old card and fit a newer more modern model in some respect. But the option like I said is not often found in mid range laptops. I will have a check but I suspect the first poster as said.