Yup.

Core i5-7500 or i7-7700 - 869/1379
Zotac GTX 1050 Ti 4GB DDR5 - 729

Done
i5-3470 can handle up to GTX 1060/RX 580. PCI Express is backward compatible.
1. FlareX is optimized for AMD. Better stability and maybe, slight performance boost.
2. I did not say better. Price is about the same.
3. Cube has less width but taller. It is aesthetics.

4. The price already tells you it has more things.
5. ITX cases usually makes the graphic card directly draw air from outside. Should not have cooling issue unless you put it on poorly ventilated area.

For additional budget, add the hard disk. I don't favor less than 7200rpm.

WD Blue 1TB
Seagate 2TB
Hitachi is banned for me due to bad warranty service.

You can use the rest of the extra money for aesthetics or GPU with better heatsink.