Adam is correct about the data plate. That being said, there is some information that can be gleaned from the VIN.
4 = Buick
Z = Riviera
87 = 2 door hardtop
T = 455 V8 4-bbl
5 = 1975
H = Flint, MI assembly plant
The remainder is the sequential production number of the car.
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Derek Thille
BCA #39416, CBC, MBCC #1984
76 Century Free Spirit Pace Car - "Spirit" / 66 Wildcat Custom Coupe - "Ellie" / 62 Special Convertible / 61 Invicta Convertible / 56 Special 4-door Sedan / 54 Century Estate Wagon / 52 Roadmaster 4-door / 41 Special 41SE Sedan / 29 McLaughlin Buick Model 51
2006 Buick Rainier - "Ruby" / 2005 GMC Sierra K2500 - "Max" (the hauler)
Thriller's Buick Page