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
You can use awk with match() to access the captured group:
$ awk 'match($0, /abc([0-9]+)xyz/, matches) {print matches[1]}' file
12345
This tries to match the pattern abc[0-9]+xyz. If it does so, it stores its slices in the array matches, whose first item is the block [0-9]+. Since match() returns the character position, or index, of where that substring begins (1, if it starts at the beginning of string), it triggers the print action.
With grep you can use a look-behind and look-ahead:
$ grep -oP '(?<=abc)[0-9]+(?=xyz)' file
12345
$ grep -oP 'abc\K[0-9]+(?=xyz)' file
12345
This checks the pattern [0-9]+ when it occurs within abc and xyz and just prints the digits.