Although not the very first, Chinese phone maker Oppo will release a five inch full HD smartphone on December 12th. The device, which is powered by a Qualcomm Snapdragon APQ8064 Quad Core 1.5GHz CPU and a Qualcomm Adreno320 GPU, will sell for around $480 in China. Several Chinese international re-sellers are also already advertising the phone for around $599 for those in the west.
As well as the quad core CPU and full HD (1920 x 1080 pixels) display, your 600 bucks get you Android 4.1 Jelly Bean, 2GB of RAM, 16GB of flash storage, GPS & A-GPS and a 12 megapixel camera. The phone can take two SIM cards, one for GSM and one for GSM+3G, however the 3G frequencies might not cover the ones in your geographical location. It supports 850/1900/2100MHz and the key missing number is 900MHz, which lots of countries in Europe use.
If you don't fancy a Chinese grey import, then there is of course the HTC J Butterfly (also known as DLX / DROID DNA) and there are rumors of upcoming full HD phones from Samsung (Galaxy S4), LG (Optimus G2), and ZTE (Nubia 5).
There is an Oppo Find 5 promotional video out there, it is all in Chinese but it is still quite fun to watch: