You can run it, and while you will get decent performance, it will not be great because the AMD APU is pretty weak. This is especially the case for the A4-5000m since it is based on AMD Jaguar cores that is basically aimed at tablet (which AMD failed to receive any design wins - not powerful enough and power consumption not low enough) and low end laptops. It is not a Richland generation APU at all using the Bulldozer CPU core. It's main competitor is Intel's Bay Trail generation Atom CPUs using in newly released 8" Windows 8.1 tablets and some 10" tablets as well.
You can read about the A4-5000m in the following link which includes some benchmarks using the integrated GPU. I will post the Skyrim benchmark using the iGPU.
http://www.anandtech.com/show/6974/amd-kabini-review
Naturally, with the Radeon HD 8570m you will get better performance in Skyrim, but gaming performance is going to be seriously limited by the 1.5GHz quad core Jaguar generation APU. Also Skyrim does not use more than 2 cores.... well it might use 3 cores, but that's "might".
Assuming the same clockspeeds an Intel CPU core is probably around 30% more powerful than a Richland CPU core. My guess is that the Richland CPU core is probably about 40% more powerful than a Jaguar CPU core. Based on this and excluding the number of CPU cores in each processor.... if an Intel CPU, Richland APU and Jaguar (Kabini) APU were all running at 1.5GHz, the relative performance compared to an Intel CPU would be as follows:
Intel CPU core @ 1.5GHz = Intel CPU core @ 1.5GHz
Richland CPU core @ 1.5GHz = Intel CPU core @ 1.15GHz
Jaguar CPU core @ 1.5GHz = Intel CPU core @ 824MHz
My advice is to avoid that laptop you are considering and go with a laptop that has either a Richland generation APU, or better yet an Intel Haswell (4th) generation Core i3 / i5 CPU.