I'm no expert, but logic seems to dictate:
- Plant trees (was 6)
- Bury corrugated drain tile for gutters to drain (was 1)
- Install underground sprinkling (was 3)
This includes the stub-outs for the sprinkler heads, but not the heads themselves*
- Install landscape beds and plants (was 5)
- Fine grading on lot to prepare for grass/sod, add topsoil as needed (was 2)
- Grass seed or sod (was 4)
Install the sprinkler heads*
This seems to me to move from the most intrusive to least intrusive.
The big ticket item - planting trees could involve delivery trucks and or skid steers driving through the yard to bring the tree to a big hole dug in the yard.
Once that's complete, you'll be tearing things up to bury the drain tile and install sprinkler lines.
Then you'll be moving potentially heavy loads of hardscape material (stone retaining walls? big bags of potting soil or mulch?) to the flower beds.
Finally, do the finish grading and planting/sodding.
Any switching of the order, to my mind, means interrupting more delicate work with more coarse work. What happens if you get an irrigation line where you discover you need to dig a hole for a tree, or you drive a skid steer across the soft ground above a freshly placed drain tile and crush it?
* Hat tip to Greg Hill for pointing these items out in the comments.