There were cruisers and battleships firing from further out but the destroyers were the ones within 5 miles, and then closer and closer and closer when they learned how much trouble the landings on Omaha were in.
http://en.wikipedia.org/wiki/Normandy_Landings
Section of this tells you about the naval forces. But yeah, they had lots of ships, Battleships, Crusiers, Destoryers, all sorts of ship. It was massive
http://en.wikipedia.org/wiki/List_of_Allied_warships_in_the_Normandy_Landings
6 Battleships
26 Cruisers
135 Destroyers and Destroyer-Escorts
A battleship, the USS Texas, closed to within 3000 yards (about a mile and 3/4ths) and took on not only German artillery, but machine gun nests as well.
“By noon, she closed the beach to about a range of 3,000 yards to fire upon snipers and machinegun nests hidden in a defile just off the beach. At the conclusion of that mission, the warship took an enemy antiaircraft battery located west of Vierville under fire.” From the Dictionary of American Fighting Ships, USN.