Q5[x_] := Abs[Re[(1 - x)^(5/2) Hypergeometric2F1[-5/2, 1/2, 3/2, 3 x/(x - 1)]]]
q5[x_] := Series[Q5[x], {x, 0, 3}]

error[x_] := Abs[Q5[x] - q5[x]]
Plot[error[x], {x, 0, 2}]