Actually, the reinstallation disk Dell sends is a full copy of Windows XP. Dell hasn't used restore disks in more than five years.
Before going this route, however, the Dimension 5150 should have a restore partition that can save you some time, if you still have the original hard drive. To access it, start the computer and as POST is finishing, press CTRL and F11, releasing both simultaneosly before you see the message "Loading Descriptor for PBR2...Done" below a blue bar at the top of the screen. If you do this correctly you should get a page allowing you to restore the computer to its factory delivered state. The process completely replaces the contents of the C drive with the original, Dell loaded, software, just like it was the day you opened the box.
If you still wish to perform this task manually you must boot from the CD. Dells normally have two possible ways to accomplish this. Start the computer and press F12 at the Dell screen during POST. When the one time boot menu appears, select CD ROM drive as the device (with the CD in the drive, of course), and press a key when you get the message to "Strike any key to boot from CD". The second way is to start the computer, press F2 during POST, and when the setup menu appears, navigate to the Boot Order menu and make the CD ROM drive number 1. Put the CD in the drive, exit setup saving changes, and press a key when you get the message telling you to strike a key to boot from CD.
Before you do any of this, however, make sure you back up anything you want to keep, go to Device Manager and note the Display Device (video card) and Modem (if you have one) as there are several of these to choose from, and if the computer is still functional, copy the C:\Dell\Drivers contents to a CD. That last contains the current drivers used in the machine and could be of some help later.
You will need to load drivers after installing Windows; you should have a Dell Resource CD that has them, but you can also find them here: Dimension 5150 Drivers.