I agree. An i5 is out of reach on that kind of budget - but a Skylake i3 just about fits the budget.
Goes a little over the $400 budget, but it's right around the same pricepoint as the one you'd suggested and it'll provide substantially better performance.
PCPartPicker part list /
Price breakdown by merchant
CPU: Intel Core i3-6100 3.7GHz Dual-Core Processor ($110.99 @ SuperBiiz)
Motherboard: MSI H110M Pro-VD Micro ATX LGA1151 Motherboard ($49.99 @ Micro Center)
Memory: Kingston ValueRAM 8GB (1 x 8GB) DDR4-2133 Memory ($28.99 @ Amazon)
Storage: Hitachi Deskstar 1TB 3.5" 7200RPM Internal Hard Drive ($44.00 @ Amazon)
Video Card: PNY GeForce GTX 960 2GB XLR8 Elite OC Video Card ($148.98 @ Newegg)
Case: Rosewill SRM-01 MicroATX Mini Tower Case ($19.99 @ Newegg)
Power Supply: EVGA 430W 80+ Certified ATX Power Supply ($23.98 @ Newegg)
Total: $426.92
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2016-07-03 00:35 EDT-0400
The PSU isn't one I'd recommend in an ideal work, but on a budget you can't really go wrong with it for <$25
Ideally I'd also suggest 2x4GB opposed to1x8GB. But on a budget, those extra couple of bucks saved can be better utilized elsewhere.
Remember though, when comparing one you want to build vs a prebuilt, you have to factor in the cost of an OS.
At this point, your build (or mine) being a little over $400, you'd be at $500 with the OS.
The positives over the prebuilt though, being you know the quality of the components (motherboard & PSU specifically) vs prebuilts who (more often than not) use lower quality components.