RaptoRSec AMD drivers on Solus are provided out of the box by the Kernel and Mesalib (OpenGL, Vulkan). You don't need to install anything.
As far as performance goes, you basically have quite a few things working against you with that model. First, it's using a 5400RPM Hard Drive and those are quite slow. That will definitely impact boot times and opening or closing programs. Second, the default RAM configuration is a single 8GB stick, but this is a dual-channel CPU. That bottleneck is bad enough on the CPU side of things, but made even worse since it is shared by the GPU. Third, the CPU itself was slow even by 2014 standards when that laptop came out and this is made worse by the memory bottleneck.
Personally, I'd recommend at least upgrading the RAM with the second stick to alleviate your memory bottlenecks. After that, an SSD would help quite a lot if you can afford it.
