What is the (tr) sign in sheet music and how to play that in the following example: https://ibb.co/GPmmNqw
The 'tr' sign means a trill (some people call it a 'shake'). It's almost certainly in brackets because the composer didn't write a trill, but the editor thinks there should be one. Because it's approached from above, the trill should start on the lower note.
I'm not sure that the editor's fingering is the best - I'd use 5 4 3 1 and trill between 2 and 3 as I suspect the next note is a D. Works better for my fingers, anyway. Your mileage may vary. [Added later] I was having a bit of a senior moment here - for some reason I was thinking in D minor. In D major 5 4 3 2 1 is probably best, but you still might want to trill between 2/3. Personally I find a thumb trill tends to produce heaviness, and this piece seems to be too lightly scored for that.