I still remember the "minimal effort" definition,
so "using only pen and paper" should not preclude using one's head as well.
I did not post my solution, since it looked d1 to me. Only after reading previous posts. I have decided to explain how it was addressed by me, and although to check my GUESS i used one line of excell, I've branded it a p&p d1 problem.
Clearly n is a 3-digit number, slightly over 133 (quick mental process of looking at the equation).
The last digit of 5TH POWER OF ANY NUMBER IS ALWAYS
the SAME AS The last digit of THAT NUMBER.
3+0+4+7= 4 mod 10
my 1st guess was 154,
lowered it to 144 and checked it (just to make it sure).
felt sorry , that it was not my 1st guess, but..what the heck...
p.s. The checking was excel-aided, could do it p&p way.