reversing a series modulo

Hello,

Reversing a series and taking it modulo 5 works, but not the opposite way
around. Why?

? f = x + x^2 + 4*x^6 + 4*x^7 + x^11 + x^12 + 4*x^16 + 4*x^17 + O(x^21)
%1 = x + x^2 + 4*x^6 + 4*x^7 + x^11 + x^12 + 4*x^16 + 4*x^17 + O(x^21)
? serreverse(f) * Mod(1,5)
%2 = Mod(1, 5)*x + Mod(4, 5)*x^2 + Mod(2, 5)*x^3 + Mod(4, 5)*x^5 + Mod(4,
5)*x^6 + Mod(2, 5)*x^8 + Mod(3, 5)*x^10 + Mod(3, 5)*x^11 + Mod(4, 5)*x^12 +
Mod(4, 5)*x^17 + Mod(3, 5)*x^18 + O(x^21)
? serreverse(f * Mod(1,5))
  ***   at top-level: serreverse(f*Mod(1,5))
  ***                 ^----------------------
  *** serreverse: impossible inverse in Fl_inv: Mod(0, 5).
  ***   Break loop: type 'break' to go back to GP prompt

Regards,
Max