Java 8 way, no loops at all:
// Given
int[] array = {-5, 8, 3, 10, 25};
// When
String[] actual = Arrays.stream(array)
.sorted()
.mapToObj(String::valueOf)
.toArray(String[]::new);
// Then
String[] expected = {"-5", "3", "8", "10", "25"};
assertArrayEquals(expected, actual);