From New Orleans

New York, May 4. TIio ITerald'sNovt Orlwans letter, 2fith uit., corifirms the statement tbat Banks had fallen back to Alex;mdria in eonsequence ef the lessening waters in lied River. All gunboats and transports, except the Eastport, are down to or below the falls, and six gunboats. which went up Black and Washita rivers to Monroe, have returned with 2,900 bales ol cottnn and 900 contrabancls, besides convoying down the steamer Euby with 4tS0 more contiabands.