The highlighted section means that with a successful driving check the driver can cause the vehicle to accelerate an amount at least 5 ft and at most its acceleration rate in 5ft increments.
For your galley, this means that you get the choice of 5ft, 10ft, 15ft, 20ft 25ft or 30ft. So long as the total speed does not exceed 180ft (the maximum speed).
If just trying to get to max velocity using the maximum acceleration (30 ft), it will take 6 rounds to get up to the maximum speed of 180 ft / round.
If you have to navigate through a fjord or something and you want to take it slow and steady, you have the option to accelerate 15 ft on the first round and then hold that speed or accelerate 5 ft or decelerate 5ft each round.