Though convection remained focused near the outer periphery of the system , the overall organized continued to steadily increase , and it is estimated the depression strengthened into Tropical Storm Florence on September 5 while located about 1120 miles ( 1800 km ) east-northeast of Anguilla . Though convection remained focused near the outer periphery of the system , the overall organized continued to steadily increase , and it is estimated the depression intensified into Tropical Storm Florence on September 5 while located about 1,120 miles ( 1,800 km ) east-northeast of Anguilla .