Will it run FM 2014? FM 2015? FM 2016? all with lots of leagues and on 5 star for speed

Case : Vantage Blue Midi Tower Case + 4 120mm Fans
Power Supply : 500 Watt With Power Cable Supplied
Motherboard : Gigabyte H81M-S2PV
CPU : Intel I5 4th Gen 4670 Quad Core 3.4Ghz (turbo 3.8Ghz) CPU
Hard Drive : 1tb Sata Hard Drive
Memory : 8gb DDR3 1600mhz Corsair Vengeance Memory
Graphics Card : Geforce GT 640 2gb (Dual screen support via DVI /HDMI / VGA)
Optical Drive : 24x Dual Layer DVD Writer
Warranty : 12 Months Return To Base (Parts & Labour)
Connections : 6 x USB 2.0 / 2 x USB 3.0 / LAN / Sound
Software : Drivers Only ( see shop for o/s options)

Yeah it should. If you're wanting to run BF4 though, that GPU won't do. It's fine for FM though.

what about an 8 core amd processor, or is Intel the way to go

Intel is generally better as most developers use it to make the game.

In order to get the best speed, you need an SSD drive. They are more expensive but they are normally between 5 and 10 times faster at loading up. So starting FM, loading databases, probably even processing matches will go by quicker because the CPU can get the information from the SSD drive quicker.