Run tests on Go 1.17.5

[aarongable]

Build a new docker container for today's Go 1.17.5 security release,
which includes a fix for the net/http package. Update our CI to run
tests on both our current and the new go versions.

[aarongable]

oh no I probably messed something up with the new go installs; looking

[beautifulentropy]

oh no I probably messed something up with the new go installs; looking

Yeah, I think go 1.17 had included backward compat for go get but on new versions it won't just warn you, it simply won't do the install.

[aarongable]

I've separated the go get --> go install change into #5846 to keep this single-purpose. I'm also moving it back to Draft because I can't actually run tag_and_upload right now because the new version of it doesn't work with rootless docker.