I see lots of examples and man pages on how to do things like search-and-replace using sed, awk, or gawk.
But in my case, I have a regular expression that I want to run
perl is the cleanest syntax, but if you don't have perl (not always there, I understand), then the only way to use gawk and components of a regex is to use the gensub feature.
gawk '/abc[0-9]+xyz/ { print gensub(/.*([0-9]+).*/,"\\1","g"); }' < file
output of the sample input file will be
12345
Note: gensub replaces the entire regex (between the //), so you need to put the .* before and after the ([0-9]+) to get rid of text before and after the number in the substitution.