“Jehoiakim king of Judah into his hand.” The conquest of Judah by Babylon was in 605 BC, and that is the year that Daniel would have been taken captive to Babylon.
“vessels of the house of God.” The “house of God” is the Temple in Jerusalem. The Temple had lots of different kinds of gold and silver vessels. Some were used to keep and or transport water, oil, wine, and blood. Some vessels were used in butchering the animals and offering them as sacrifices. Also, the priests got to partake of some of the offerings, so some were used by the priests when they ate and drank. It was some of these holy vessels that Belshazzar had brought to his banquet hall to drink from when God wrote on the palace wall and pronounced his doom and the doom of his kingdom.