If you're creating at 300 ppi, that's "per inch" so if the width is 5 inches, that would be 300 x 5. Then if the height is 4 7/8 (4.875), that would be 300 x 4.875.
To get 5" x 4 7/8", you have (300x5) x (300x4.875).
To make things even easier, just create your document in inches. Then you can go to the Image Size dialog box and change the units to pixels. It will show you the dimensions.
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Cassie
My Gear: Nikon D300s w/18-200mm VR & 50mm 1.4
Software: Adobe Photoshop CS4, PSE 6, Lightroom 2