WHICH GRAPHICS CARD IS BEST FOR a10-5800k THAT CAN RUN DOTA 2 at max settings

Budget....?
PSU....?

include some of these stuff next time it helps your answer get solved faster

You really won't be able to no matter the Video card because the A10 (a APU) will bottleneck any performance you hoped the video card would 'make up for'. Remember data code is stored (HDD) then read (RAM) in chunks to be processed (CPU) to determine what component (Sound, NIC, GPU) will use the code to perform the task, all before the GPU gets involved. If you have a A10, you would need to replace the computer with either a AMD 8xxx or a i5 based computer to 'game'. i3 (except the brand new Haswell)/all other AMDs dont' have enough performance for 2013 games, and i7 (what games are 'benchmarked on' and 'gamers play on) is probably too expensive for you.

You sir are giving this guy no hope at all.. atleast try to research a bit and see what cards go well with A10..

Did you know the Sandy Bridge Core i5 and i7 are APUs? however intel refrains from calling it so and just keeps the name CPU.. whether the A10 is an APU or not, once a GPU is POST by the system that integrated GPU is disabled

Yes I just read up that the new HASWELL incorporates the GPU chipset onto the layer of the CPU because they had tossed out the old chipset which wouldn't work well with HASWELL. The new INTEL HD is meant SPECIFICALLY for Ultrabooks, which are predominant marketplace sellers (laptops still outsell desktops 3 to 1) so that a lightweight, lower power (more battery life) and less heat laptop can be produced that doesn't need a dedicated video card. The fact that same CPU can be used in a desktop is just a simplification of design processes to alleviate duplication and increased costs to Intel.

The APU (read up on it yourself plenty of material) was SPECIFICALLY designed to be a LOW power combined (reason AMD bought out ATI) combo CPU and GPU for portable units, at a low price point; specifically the netbooks and tablets. The use of the APU on the desktop platform was to generate a low cost 'generic' PC for at the i3-Clarksdale / Sandy Bridge performance level (your A8 and A10s) alternative to Intel based PCs. The APU is NOT in anyway made for gaming.

I answered a couple posts already with links to scores, a APU core itself can handle up to 2009 games (5 years ago) 2010 games push it beyond playable (single FPS to tens FPS) OR 'will not play' on it, and forget anything like a 2013 game. EVEN with a GPU added on, as I noted, the GPU does not 'read the data' directly from the HD (basic 101) so it can't "bypass" the processing the CPU had to do, which it can't for any games.

http://www.tomshardware.com/reviews/a10-6700-a10-6800k-richland-review,3528-6.html
Here is some scores FYI, and NOTE "we had to drop the quality settings as low as they go " to get those scores.

Now take AC4, Ghosts, BF4, whatever they all demand the CPU is INVOLVED with making the game work, not 'the best GPU no matter how crappy a CPU you have'. In fact BF4 is purposedly called a CPU HOG, because so many people are trying to play it on AMD 6xxx cores, and can't believe they are getting such crappy results when "BF3 never gave me as many problems". Apples vs Oranges and forgetting the CPUs are now part of the game, not just the GPU.

First of all BF4 is broken as it is, and you should know that well enough. It's not optimized fully yet and still as issues.

What you saying for this guy is that there is no hope for this guy with his current CPU, B.S if you ask me, he can buy a 7870 Ghz edition just fine to work with it and play 2013 games fine on low-med settings with his 'APU'. You fail to comprehend with what im saying.. the GPU within this CPU will disable the moment a dedicated video card is detected by the system, rendering the CPU just a CPU. The A10 is just a CPU with a GPU integrated just like a Core i5 or Core i7 when a video card is detected with either of these CPUs the integrated GPU is disabled.

They are already videos of people gaming with this A10 while using a GPU with it and no problem.
The A10 is a APU and so is the Core i3/i5/i7.

Stop killing this guys chances and actually answer his question

BF4 has been reliably played and tested, so don't write it off as 'broken and doesn't work' if that was true the press would have field day with EA multiple lawsuits by consumers over false advertisements / bad product. It does work, and is being played as we speak, the link I did provide (if you looked) uses the standard Metro Last Light test, as well as Tomb Raider and the APU WOULDN'T ALLOW THE GAME TO WORK UNLESS AT LOWEST GRAPHICS LEVEL. WHY?

No I am not failing to comprehend how your bypassing the GPU in the APU by adding a GPU seperately; YOUR failing to to comprehend disregarding that it (APU) as any impact what so ever as long as he has a 'mighty GPU'. If you bothered to look at the scores, which INCLUDE using a GPU to 'bypass' the APU (as you naively believe) did nothing more then give a extra 4FPS because the APU still bottlenecks any GPU when compared to say a i3, i5, AMD8xxx or heavens forbid a i7.

Basic 101: Data Code is stored (HDD) to be read (RAM) in chunks for processing (CPU) before handed to a component (Sound, Printer, NIC, GPU) to perform that code's instructions. So before you GET to a GPU you have these other players involved, the GPU does not handle the game ALL BY ITSELF. In 2013 games the coding for 'smart AI' and other things is NOT a GPU rendering task, it is a CPU TASK. Hence why all the AMD Fanboys with 6xxx are crying alot about how they can't get great BF4 play (for example) no matter if they put in a R9 or a 780 as compared to a i5/AMD 8xxx or better yet i7.

The APU is targetted to compete against a i3-Clarksdale / Sandy Bridge with Integrated Graphics performance level , I would never suggest someone use the old i3s for gaming because they were made for general (grandma emailing and looking at facebook pictures) computer use, not gaming. To suggest that the APUs would be any different is ignorant.

ANY benchmarks shows the same things: i3/rest of AMD CPUs for general (grandma doing email) usage, i5/AMD 8xxx for moderate gaming level, i7 for performance gaming (and best suited for R9/Titan cards so as not to bottleneck the GPU). That is the facts, look for yourself.

If someone got themselves a APU, they have really no choice, just as much as if they had a Intel i3 Clarksdale, a Intel Duo Core 2, or if they were using a Pentium 4 CPU, they would need to replace the computer FOR GAMING (not for other general uses) especially if they intend on any 2013 and forward games.

King James good luck

I bought gigabyte 6670 2GB here and the performance is amazing! Try this 2Gb version which is the BEST A10-5800k compatible graphic card.
http://www.rctoysshop.com/en/computer-hardware-pc-accessories/198-gigabyte-6670-2gb-amd-radeon-gv-r667d3-2gi.html