You can get there using vertex snapping and some manual rotation.
Make your base tile a single face pentagon. Remove double vertices (there are some).
Don't use object instances yet, you'll convert them all in the end. Just copy new tiles now.
The main angle is 71°. Type the equations directly into the rotation field.
Enable Vertex Snapping > Median. ...
You can easily rotate the view by pressing the middle mouse button and moving the mouse. To pan the view, do the same but also maintain Shift. To zoom in/out, do the same but also maintain Ctrl (or simply use the mouse wheel).
You can use the numpad keys to set the view to :
front 1, back Ctrl+1
right 3, left Ctrl+3
top 7, bottom Ctrl+7
In Blender 2.79 and before, the cursor is supposed to go wherever you click with LMB.
In Blender 2.80+, left-clicking selects the object. Right-clicking will give you editing options for the object selected.
Also in 2.8+, the cursor should not go wherever you click with LMB.
What most likely happened, is that you accidentally have "Cursor" selected in ...