Unintended reaction: Sketch makes LEDs turn on and of randomly/LEDs don't react
Your code has a serious bug here:

if(button == HIGH){ 

    digitalWrite(act_pin[j], HIGH);

    j = j+1;

    button = LOW;
}


You increment j without any boundary so it will have the following cycling values:

0, 1, 2, 3 ... 32767, -32768, -32767 ... -1, 0 ...


Hence, quickly act_pin[j] will return garbage...

The solution is easy, you must limit j to [0,1,2,3,4], just replace the j = j + 1 line as follows:

j = (j + 1) % 5;


% is the modulo integral operation that will give you the reminder of dividing j by 5, which is always strictly less than 5, and it cycles as you want.