The pseudo-ε-expansions for the coordinate of the fixed point g*, the critical exponents, and the sextic effective coupling constant g₆ are determined for the two-dimensional Ising model on the basis of the five-loop renormalization group series. It is found that the pseudo-ε-expansions for the coordinate of the fixed point g*, the inverse exponent γ^-1, and the constant g₆ possess a remarkable property, namely, the higher terms of these series are so small that reliable numerical results can be obtained without invoking Borel summation.