How I would do it is, Change the fan profile first.
Set it so fan is 100% on at 85C since once you get past 75C with Barts core stability goes down hill fast.
Then do as krisco65 has said, But also keep checking temperatures as your doing it. Ideally you want to keep it below 85C.
Also before your set on a final core clock run a bench mark like 3d mark 11 since Iv found furmark is always stable a little higher then benchmarks/games because it doesn't fully load the memory controller.
Once you have verified its fully stable EG runs a game for a hour no problem move on to overclocking the memory.
Drop the core 5mhz lower then where you found it to be stable and do the memory. Dont use furmark to stress it when overclocking memory since furmark puts no load on the memory or memory controller. Personally I do 3d mark 11 runs to find make memory overclock.
Then once youv found the point it crashes/artifacts (weird colours/glitches) lower it by 30mhz since the memory has error correction which slows the card down when its with in 10-20mhz of being unstable.
If temps are still good you can push the core voltage a bit higher which gives you more room to overclock the core but not the memory. With stock cooling youll most likely be limited by the temp once you play with voltages.