I never have measured the dimensions of the hard drive, but the form factor standards ensure that available drives will fit in the bay, the screw holes will line up, and the standard cables and connections will plug in.
I have never heard of a 2 5/8'' drive. As Freebooter mentioned, the form factor standard is stated 2.5'' and will fit in your PC.
Actual Dimensions
A 2.5-inch SATA hard drive actually measures 2.7 inches wide, 0.37 inch tall, and 3.96 inches long. According to The Tech Report, the 2.5-inch designation actually refers to the size of a typical laptop drive platter, the disc inside the housing that data is actually recorded on. The average 2.5-inch drive weighs slightly more than 4 ounces.