My wife has a 52cm Ruby with 105 components. I have a 58cm Roubaix with 105. Both are triples. When she is in her middle chainring and the small rear sprocket she gets a predictable but irregular "ping" that took a long time for me to figure out. It turns out that the chain is -just- hitting the outer chainring where the chain ring has small, circular metal tabs that protrude inward. The chainring has small circular metal tabs (four of them) in the area -just- below the teeth. If the crank arm is set to 12 oclock the tabs are at about 2, 4, 8 and 10PM. There is another set of four tabs that are in a circle just inside these outer tabs and just past the outer tabs so they lie around 2:30, 4:30, 8:30 and 10:30 oclock. Those tabs protrude to the inside of the chain ring but don't touch the chain.
The problem doesn't happen on my bike, probably because of a slightly longer chain stay? I have always been pretty anal about my bike being silent and have imparted that sense to her... so this is a bit of an irritant. Shifting to the outer chainring and moving up three cogs in the rear gives her virtually the same gear admittedly but it's an irritant. I'll guess a .5mm change would be all that's needed. Can a thin shim be added to the driveline side to push out the chainrings? I don't want to go crazy on this...just looking for a reasonably simple solution if it exists.

There are bottom bracket spacers that will move the crank out 1, 1.5, 2 mm etc. They are very easy to install, you won't even need to break the chain.

Moving the entire crank out may solve your problem, and it definitely will if you move it far enough, but I don't think it's a matter of less than 1mm.

The chain coming from 4+ mm farther out and as you move the crank out both rings are moving together. You might be able to shim it easily dopending on the vintage of 105, modern external BBs being the easiest.

The other option is to make 5 thin spacers (here 1/2mm is probably enough) and move the outer chainring out that far, increasing chainring separation. Don't get carried away, too much space and the chain can crop between the rings on downshifts.