Could someone inform me about the exact operational costs of a flight hour for this specific type of aircraft?
The Gulfstream G550 is a variant of the Gulfstream V.
From aopa.org (November 16, 2015) for the G550, it costs $4,731.05 per hour, give or take. (Assuming the plane is paid for already.)
Adjusted for inflation that's $4,825.11.
Note that the GV is older than the G550, and would generally cost more to operate.
This figure includes fuel, maintenance (parts and labor), engine reserves, auxiliary power units if applicable, and miscellaneous expenses to include crew travel, catering and cabin supplies, landing and parking fees—all boiled down to a single number.