You can and you can't. Boat Tech has access to Merc's database.
There are some lists out there, mostly cobbled together.
Yours is a Merc/Mariner, as opposed to the Yamaha Mariners (which Yami built for Merc).
Merc's don't really have "serial numbers", they simply have "production numbers" - so the next motor off the assembly line gets the next number (not quite but you get the idea).
Anyhow, the horsepower, year etc is not "encoded" into that production number.
That's good if you are a Merc dealer because you never have "last years model" on the floor. Your particular model belongs to the production run that ran from late 1985 (new 86 models) up until the middle of 1994 (when they made some minor changes).
So if your 87 model happened to sit at the dealer until say, 1991, it would have been sold as a brand new 1991 model and the warranty would start the date of sale.
So....
the easiest way to find the year is to post the (serial) up here and one of us will give you an answer. Boat Tech has the real database, a few others of us have "pretty good" production lists.