The search path already allows more than 5 tags, and it uses OR logic. From the docs:
tagged and nottagged are semi-colon delimited list of tags. At least 1 tag in tagged will be on each returned question if it is passed, making it the OR equivalent of the AND version of tagged on /questions.
(bold added)
Note that tags are separated with a semicolon, not a comma. So, you would use:
/2.1/search?pagesize=100&page=1&order=desc&sort=creation&tagged=linux;ubuntu;bash;linux-mint;mint;linux-distributions;linux-distro;archlinux&site=superuser&filter=.Ericv1w97*YhCWfY.uMVBr(o
**[which works fine (try it)][2].**