The problem is in the last line:
Sierra is incompatible with CS5.5.
I have both Photoshop + Illustrator open and working --- I got the computer at Christmas and In Design was working until 2 days ago despite what Adobe says. Makes no sense that both Photoshop + Illustrator in the same version are working. The entire Adobe Creative Suite opens except for In Design????
You're on your own to try. But it doesn't work for most people.
CS5.5 is end-of-life and unsupported. Operating systems developed after CS5.5 can be problematic, especially on a Mac.
I just called Adobe Sales since Support was not an option. Was told both Photoshop + Illustrator are nearing their end --Another month or so he said they would stop working as well so may just do In Design cloud for 1 month until the other apps stop working. THANKS!!!