$str = "07:56:05 [Text 1][Text 2] Text 3 [Text 4][Text 5] Text 6:(6,37,70)";

preg_match('/^\d\d:\d\d:\d\d\s*\\[([^\\]]*)\\]\\[([^\\]]*)\\]\s*([^\\[]*)\s*\\[([^\\]]*)\\]\\[([^\\]]*)\\]/', $str, $array);

echo "<PRE>";
print_r($array);

Результат
-----------------------
Array
(
    [0] => 07:56:05 [Text 1][Text 2] Text 3 [Text 4][Text 5]
    [1] => Text 1
    [2] => Text 2
    [3] => Text 3 
    [4] => Text 4
    [5] => Text 5
)

$result = array
	(
		trim( $array[ 1 ] ),
		trim( $array[ 2 ] ),
		trim( $array[ 3 ] ),
		trim( $array[ 5 ] ),
	);

print_r($result);

Результат
-----------------------
Array
(
    [0] => Text 1
    [1] => Text 2
    [2] => Text 3
    [3] => Text 5
)