Is everything in this build compatible/makes sense?

I have changed it a bit so it's 50$ more expensive now, but will perform better and last longer.
PCPartPicker part list / Price breakdown by merchant

CPU: Intel Core i5-6500 3.2GHz Quad-Core OEM/Tray Processor ($192.99 @ SuperBiiz)
CPU Cooler: Cooler Master Hyper 212 EVO 82.9 CFM Sleeve Bearing CPU Cooler ($29.38 @ OutletPC)
Motherboard: Gigabyte GA-B150M-DS3H Micro ATX LGA1151 Motherboard ($65.38 @ Newegg)
Memory: Crucial Ballistix Sport 8GB (2 x 4GB) DDR4-2400 Memory ($37.99 @ Adorama)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($47.49 @ OutletPC)
Case: Corsair 200R ATX Mid Tower Case ($55.98 @ Newegg)
Power Supply: XFX XT 500W 80+ Bronze Certified ATX Power Supply ($53.98 @ Newegg)
Optical Drive: Asus DRW-24B1ST/BLK/B/AS DVD/CD Writer ($16.88 @ OutletPC)
Operating System: Microsoft Windows 10 Home OEM 64-bit ($83.89 @ OutletPC)
Total: $583.96
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2016-07-31 06:40 EDT-0400

Also,
there is no video card. is it on purpose ?
 

TheOnlyCortez

Commendable
Jul 30, 2016
16
0
1,510


The graphics card will be an RX 470
 

TheOnlyCortez

Commendable
Jul 30, 2016
16
0
1,510


Cool! This is kinda a random question but would this run Grand Theft Auto 5?

 
Yeah.
May be not on highest settings, but it will.
If you are gaming on 1080p monitor, the GTX 1060 for 250$ would be ideal card, but you can always upgrade the GPU later.
You have a very solid build that will perform great.
Next step would be adding SSD, but guess you already planned that as well :)