Given it's an FM2+ motherboard and a prebuilt system, it seems fairly safe to assume there isn't a worthwhile upgrade. There is so little differentiation between the CPUs higher in the product stack making any upgrade difficult to justify financially.
To keep costs down would mean salvaging as much as possible for a 'new' build. To me this suggests a secondhand 4th gen Intel and compatible motherboard. I do anticipate an issue with Windows licence too which incurs its own cost.