I'd consider something like this:
PCPartPicker part list / Price breakdown by merchant
| Type | Item | Price |
|---|---|---|
| CPU | Intel Core i5-2400 3.1GHz Quad-Core Processor | Purchased For $0.00 |
| Motherboard | Asus P8H61-M LE/CSM R2.0 Micro ATX LGA1155 Motherboard | Purchased For $0.00 |
| Memory | Corsair Vengeance 8GB (2 x 4GB) DDR3-1600 Memory | Purchased For $0.00 |
| Storage | Crucial BX100 500GB 2.5" Solid State Drive | $159.99 @ Amazon |
| Video Card | XFX Radeon R9 390 8GB Double Dissipation Black Edition Video Card | $294.98 @ Newegg |
| Case | Thermaltake Core V21 MicroATX Mini Tower Case | $59.49 @ Amazon |
| Power Supply | EVGA 750W 80+ Bronze Certified Semi-Modular ATX Power Supply | $49.00 @ NCIX US |
| Operating System | Microsoft Windows 7 Home Premium SP1 OEM (64-bit) | Purchased For $0.00 |
| Prices include shipping, taxes, rebates, and discounts | ||
| Total (before mail-in rebates) | $623.46 | |
| Mail-in rebates | -$60.00 | |
| Total | $563.46 | |
| Generated by PCPartPicker 2015-08-16 10:17 EDT-0400 |
Sandy Bridge i5s are still perfectly fine for gaming. CPUs have not improved as much as GPUs have in that timeframe, so you'll find the gains from upgrading that minimal compared to what you'll have to pay for a new CPU, mobo and RAM if you go Skylake. Here are a bunch of CPU benchmarks in games to give you a better idea:
http://www.techspot.com/review/991-gta-5-pc-benchmarks/page6.html
http://www.techspot.com/review/1006-the-witcher-3-benchmarks/page5.html
http://www.techspot.com/review/979-battlefield-hardline-benchmarks/page5.html
http://www.techspot.com/review/1000-project-cars-benchmarks/page5.html