I hear Skyrim is CPU-intensive, so I think you need a far more powerful CPU - like an FX6300, if you stick to AMD. Also, think of getting a Radeon 7750 at least (the 7750 is the fastest card that doesn't need extra power connectors).
On highest settings at 1080p? Get a a Radeon 7870, I think.
Skyrim is both CPU and GPU intensive. The A4-5300 should be adequate enough from a CPU perspective; overclocking will improve it's performance.
However, the integrated iGPU (Radeon HD 7480D) is weak. Not much more powerful than a desktop Radeon HD 5450. Intel's HD 4000 graphic core is better. You definitely need a dedicated GPU for that.
I started playing Skyrim last week with my system below. It is patched to version 1.9 and I also have the official HQ texture pack installed. I can get consistent 55 to 60 FPS with my Radeon HD 5850 1GB from Sept 2009 and playing at 1920x1200 resolution. However, using the HQ texture means 1GB of VRAM is really not enough so from time to time the game actually stutters. For now I am trying to decide if I want to drop down the graphics quality to medium or disable the HQ texture pack. If my HD 5850 had 2GB of VRAM, then there would not be any issues.
I suppose the question is how much money are you willing to spend and what resolution do you play games with?