The five barrel guns are called funflings--funf means five in German
The four barrel guns are called vierlings--vier means four in German.
The three barrel guns are called dreilings--drei means three in German.
Drillings, the anglicised version can be three barrels side by side i.e.0-0-0 or 2x1
0-0/0.
Please note that they can be all shotgun barrels, all rifle barrels, they can be all the same calibre or all different calibres and bores...I've seen one drei that had three different calibre rifle barrels and another vrie with four different calibre rifle barrels.
Most common drie are 2x the same over a single.
We have a 2x.303 over 16 bore as well as 2x16 bore over .303
The way they are configured is also how they are described in German.
Hambrush Arms barrel configuration
A shotgun beside a rifle was normally called a Cape Gun and they aren't that common anymore...Two rifle barrels the same are the most common especially in O/U...three barrel jobs are the most common of combination guns...four barrel guns are still quite rare.
IIRC there are exactly six, five barrel jobs that were ever made and five were made by Peter Hofer and started at around 250,000 Euros or about $361,000 to 400,000 Euros or $578,000...I know one of his vierlings sold for $1 million.
I have never heard of or seen anything with more barrels in a hunting gun, not that there might not be some but I've never heard of or seen them.