  We use Asymptotic Pade Approximants (APAP's) to predict the four- and
five-loop \beta-functions in QCD and N=1 supersymmetric QCD (SQCD), as well as
the quark mass anomalous dimensions in Abelian and non-Abelian gauge theories.
We show how the accuracy of our previous \beta-function predictions at the
four-loop level may be further improved by using estimators weighted over
negative numbers of flavours (WAPAP's). The accuracy of the improved four-loop
results encourages confidence in the new five-loop \beta-function predictions
that we present. However, the WAPAP approach does not provide improved results
for the anomalous mass dimension, or for Abelian theories.
