This verse is about three significant places in Israelite history... which were still quite important when Amos was writing.
The questions on the sheet...
What happened in biblical history in this place?
Why would people have thought of it as holy?
Beersheba: why does the verse say “journey to”, not just “go to”?
Gilgal: there’s something striking in the Hebrew of this verse that you don’t see in the English translation. What is it?
Bethel: what does the name mean? What was a contemptuous name for it (see Hosea 4:15, 5:8, 10:5)? So why does Amos prophesy about Bethel as it does?
Places where you might find answers...
All the usual ones (e.g. Bible Gateway, BibleHub, StudyLight) but also:
http://bibleatlas.org - part of BibleHub where you can investigate places and locations
http://www.bibleplaces.com - background on particular places mentioned in the Bible
http://www.biblestudytools.com/dictionary/ - articles on lots of subjects (names, places, events, doctrines, and much more)
https://www.biblegateway.com/resources/commentaries/?source=1 - a few commentaries on Bible books where you can look up Amos 5:5 and get some expert information or hints about the meaning of the verse (from this list, try the Asbury Bible Commentary or the Reformation Study Bible)
http://www.studylight.org/commentaries/guz/amos-5.html - David Guzik is one of the clearest and simplest commentators around today; this is his take on Amos 5.
http://biblehub.com/commentaries/amos/5-5.htm - older commentaries here, giving you their wisdom on Amos 5:5 all on the same page. Some good stuff here you won't find elsewhere too.