Black nationalist guerrillas based in Mozambique made a rocket and mortar attack on Rhodesia's third largest city, Umtali, Sunday night, military spokesmen said.

It was the second attack on Umtali, a town of 8,000 whites and 40,000 blacks, since early September. As in last month's attack the guerillas launched their missiles at 10:20 p.m. from the Umtali Height's a range of hills overlooking the city from the north.

Five persons were injured in the 40-minute attack, the Rhodesian military command said in Umtali, which is located three miles west of the Mozembique border.

About 50 rocket and mortar shells landed in the five-square-mile white residential area of Umtali, military spokesmen said. The same sources said the attackcame from Robert Mugabe's Mozembique-based wing of the Patriotic Front, which is seeking to overthrow the white-dominated biracial Rhodesian government of Prime Minister Ian Smith .

Rhodesian military forces yesterday dropped helicopter-borne paratroopers in the hills surrounding Umtali as spotter planes flew overhead.

In Canberra, Australia, immigration officials said yesterday that the number of white Rhodesian seeking to immigrate to Australia has risen sharply in the past three months. More than 700 Rhodesians have applied to come to Australia compared to 1,000 in all of last year, they said.