Is 5600 hours on twin Volvo yamd63p 370hsp something to worry about on a 1998 trawler?

You have to know the maintenance schedule per the owners manual to know if that is a lot of hours on the rig and engine(s). If that was a car engine going 70 MPH on the highway, it could have logged 392,000 miles. 

iT CERTAINLY COULD BE. BUT IT DEPENDS ON HOW GENTLY THEY'VE BEEN TREATED AND HOW WELL MAINTAINED. I've seen Volvo marine diesels go ten thousand hours and I've seen them trashed in as little as two thousand.

The average marine gasoline engine runs for 1,500 hours before needing a major overhaul.

The average marine diesel engine will run for more than three times that long and log an average 5,000 hours under the same conditions.

Check the engine Log-Book.