To be honest, I doubt you'd see that much of an improvement on that system, especially with an i5-3470. And with it being a refurbished Dell that's using an Ivy Bridge CPU, I don't see much upgrade path for it either. And I have to agree that I'm not sure you'd get that much used for your system.
That being said, it's hard to tell which MSI board you currently have...but if it's this one (https://www.msi.com/Motherboard/support/970A-G46.html#support-cpu) you always have the option of getting an octa-core chip. An FX-8320 (like mine) has the same speed as your current FX-6300, but gives you 2 extra threads for some improved multi-threaded performance. Or you can even get the FX-8350 or 8370, which run even faster.
Or, if you can save up money & wait at least a month, you can see how Ryzen compares to Haswell/Skylake/Kaby Lake in performance & price, & decide if you want a brand-new build from there.