$500 bucks can get you this:
PCPartPicker part list /
Price breakdown by merchant
CPU: Intel - Pentium Gold G5600 3.9GHz Dual-Core Processor ($93.00 @ B&H)
Motherboard: MSI - B360M PRO-VDH Micro ATX LGA1151 Motherboard ($70.98 @ Newegg)
Memory: Team - Vulcan 8GB (2 x 4GB) DDR4-2400 Memory ($86.89 @ OutletPC)
Video Card: EVGA - GeForce GTX 1060 3GB 3GB GAMING Video Card ($248.90 @ OutletPC)
Total: $499.77
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2018-05-02 23:50 EDT-0400
Few words
While G5600 isn't as good as i5-8400 is, it's cheaper than Core i5 and it's also better performing than your current CPU. So, going with G5600 is a worthwhile upgrade,
i3-4130 vs G5600, comparison:
http://cpu.userbenchmark.com/Compare/Intel-Core-i3-4130-vs-Intel-Pentium-Gold-G5600/1621vsm469126
Put in B360 chipset MoBo that doesn't have bells and whistles to jack up the price. But what it has is 4x RAM slots. And thanks to this, you can upgrade your 2x 4GB (8GB) RAM amount easily in the future if the need arises. Oh, the RAM is 2400 Mhz and it has CAS Latency of 14, making it more responsive than e.g CL15 and CL16 RAM kits.
Since GTX 1060 6GB GPU would've blown your budget, i put in GTX 1060 3GB GPU. While it doesn't have 6GB of VRAM, it's 3GB of VRAM is still enough to play today's titles with high/ultra settings @ 1920x1080 with solid 60+ FPS. In my Skylake build (full specs with pics in my sig), i too have GTX 1060 3GB GPU but mine is MSI Gaming X version.
Oh, GTX 1060 3GB GPU is also 3rd best GPU there is when it comes to the value (price to performance ratio). Only GTX 1070 Ti and GTX 1080 have better value than GTX 1060 3GB GPU has. While GTX 1060 6GB GPU is at 6th place when it comes to the value.
Or if you don't want to hassle with MoBo replacement, you can go for these two:
PCPartPicker part list /
Price breakdown by merchant
CPU: Intel - Core i5-4570 3.2GHz Quad-Core Processor ($217.65 @ Amazon)
Video Card: EVGA - GeForce GTX 1060 3GB 3GB GAMING Video Card ($248.90 @ OutletPC)
Total: $466.55
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2018-05-03 00:04 EDT-0400
Again few words
i5-4570 is a bit better performing than G5600 and can be a viable upgrade. Especially since you can keep your MoBo and DDR3 RAM,
i3-4130 vs i5-4570, comparison:
http://cpu.userbenchmark.com/Compare/Intel-Core-i3-4130-vs-Intel-Core-i5-4570/1621vs2770
G5600 vs i5-4570, comparison:
http://cpu.userbenchmark.com/Compare/Intel-Pentium-Gold-G5600-vs-Intel-Core-i5-4570/m469126vs2770
In my Haswell build (also, full specs with pics in my sig), i have i5-4590 which is about 3% better than i5-4570 which i have paired with GTX 760 (GTX 760 is about 81% worse than GTX 1060 3GB GPU). Despite older hardware, my Haswell build is handling today's games just fine with high settings @ 1920x1080 with 60+ FPS.
Bonus:
Here's comparison between both of my suggestions. Latest tech as a base and old timer as an alternative:
Userbenchmark PC Build Comparison
Baseline Bench: Game 60%, Desk 57%, Work 34%
CPU:
Intel Pentium Gold G5600
GPU:
Nvidia GTX 1060-3GB
HDD:
WD Blue 1TB (2012)
RAM:
Corsair Vengeance LPX DDR4 2400 C14 2x4GB
Alternative Bench: Game 56%, Desk 51%, Work 22%
CPU:
Intel Core i5-4570
GPU:
Nvidia GTX 1060-3GB
HDD:
WD Blue 1TB (2012)
RAM:
G.SKILL Ripjaws DDR3 1600 C9 1x4GB
Latest tech performs a bit better because it has double the RAM to go around. Other than that, both have pretty equal performance.