What's up everybody? I'm pretty familiar with Linux terminal window operation because it's part of my job; however, this is my first time setting up a Linux workstation from scratch. I don't have an extra computer lying around so I've installed Slackware 13.37 on VirtualBox on my laptop.
The install went just fine but that's about as far as I've successfully gotten. I figured that a good next step would be to install and configure graphics drivers, and that's where I ran into issues. I've been browsing forums and searching google but I couldn't really find anything pertinent to my problem.
I downloaded the latest drivers for my ATI Mobility Radeon HD 5650, built the package from AMD's .run driver file, and installed the package to the /usr/src/ati directory. Next I ran the aticonfig -initial command and all I get back from the shell is the message: "No supported adapters detected."
Note: before downloading the driver I ran the xorgsetup command (xorgconfig command was not found) but that's about it.
I don't have any idea where to go from here so I would really appreciate some help. Thanks!

You are running Slackware in Virtualbox, a software that emulates a complete PC. The hardware in that PC is also virtual and, except the CPU, has nothing to do with your physical system. That is the reason why the AMD driver won't work, there is no AMD graphics in the virtual machine.
In fact, graphics should work out of the box, with the slow vesa drivers. If you want better graphics support install the Virtualbox Guest Additions on the virtual Slackware.

Sorry, I forgot to mention that I do have Guest Additions installed and Hardware virtualization applied in the system acceleration settings. Thanks for the Reply though!

Well, then just launch the GUI with startx. If that doesn't work please post any error messages you get.

Turns out that I didn't have the Guest additions installed properly. I reinstalled them properly and then the proper card showed up in lspci. Before then the only devices listed for graphics were vesa. Also had to edit the xorg.conf file to add my screens resolutions because the X window was only listing up to 800x600.