I'm new to SlimDX and working in a legacy system. There's a Direct3D11 device being used, but I'm trying to use CreateSphere from:
SlimDX.Direct3D9.Mesh.CreateSphere(Direct3D9.Device,...)
Is there any way to use CreateMesh with a Direct3D11 device? Casting to Direct3D9.Device is not a valid cast. I don't understand why a newer API would remove a feature as simple as creating a sphere.
The problem with your question is that you're mixing up two very distinct things.
The DirectX API didn't have a CreateSphere method, ever. This was contained in a helper library, DXUT, which was discontinued by Microsoft.
Just write your own or use a pre-made mesh. If you don't know how, you were probably relying too much on the helper libraries anyway.
Of course, your level of understanding is betrayed by the feeling that creating a 3D sphere is somehow a simple task. It's not. There's tons of different ways to generate even 3D primitives that depend a lot on what you're doing, that's probably one of the reasons DXUT was discontinued in the first place. There's many ways to arrange the vertices of a sphere (UV sphere, Icosphere, ...), many ways to index those, many different vertex formats which need to be filled differently based on what you're doing.
It still made sense to have those helper libraries when these problems simply weren't there - before the days of the programmable graphics pipeline. The old fixed pipelines were pre-made for relatively simple tasks, today you have much more flexibility, for some cost in having to understand how some things are done - things like HLSL, texture mapping, light calculations etc.