Flash floods spawned by two days of hard-driving spring rains forced at least 5,000 persons from their homes in Mississippi and Alabama yesterday and overflowed rivers and streams across the Southeast.

President Carter declared a state of emergency in Mississippi so 145 federal mobile homes could be donated to the state to provide temporary housing for families who lost their homes.

At least nine deaths-four each in Mississippi and Alamba and one in Georgia-were blamed on the flooding from unusually heavy rains that began Wednesday night and ended Friday.

In Alabama, the Red Cross said 1,000 families were staying in special shelters yesterday, and disaster crews were sent to Tuscaloosa, Birmingham and Wetumpka, north of Montgomery.

Alabama Civil Defense officials said that as many as 1,000 people were evacuated from southern Sumter County, in west-central Alamaba, because of two earthen dams bursting in neighboring Mississippi.

In Tuscaloosa, where the downtown area reported more than 10 inches of rain, County Commissioner Bobby Miller said damage countywide would 'go into the millions of dollars.'

The Tombigbee and Luxapallila rivers overflowed their bands in Columbus in northeastern Mississippi, dividing the city and driving 2,000 persons from their homes, said Lowndes County Civil Defense Director Ray Gildea.

The flooding in Columbus cut off direct access between the east and west parts of the city, forcing motorists to detour 65 miles through Alabama.

In Jackson, Miss., authorities said 500 families were evacuated when the Pearl River rose to 38.8 feet by noon yesterday. Workers struggled to build a two-mile-long wooden barricade to keep the river from swamping the city's water treatment plant.

Backwaters from the swollen Mississippi River forced hundreds from their homes at Vicksburg, officials said. CAPTION: Picture, Two waders check damage done to some Birmingham residences by heavy flooding. UPI