Commercial photography is all about building brands. You have to be a master at the technical and artistic aspects of photography to receive a commercial photography assignment and successfully produce the desired result. Think about what you want to specialize in as commercial photography includes a wide range of distinct areas. If you want to focus in on product photography, think about and develop a personal style that can set you apart from the competition.
The equipment is important, but it isn't the main thing that will make you successful in this area. The lenses themselves can range from ultra wide angle to medium telephoto and likely will land right in the middle for most assignments (24-100mm in 35mm equiv fov). If you are photographing small objects or want detail shots, consider a macro lens. The camera body, while important, isn't going to make or break the success of your business. I would imagine you will find the D5200 limiting in many cases as you progress. A full frame camera will be a drop in the bucket as far as cost to a successful business. Work with the tools that make your job easier and more efficient but also allow you to capture what your vision. The D5200 may successfully do this for an amateur for years.
If you are going after product photography what you really need to focus on is lighting and not your camera body or lenses (although you need at least the basics). See this question for more information: Lens Advice for Product Photography
Finally, I don't know what courses or lessons you have had in the past, but I can recommend at least one great resource around general commercial photography if you haven't utilized it yet: Commercial Photography: From Start to Finish with Joel Grimes