!Spoilers Inside!
It starts like this:
!Spoilers Inside!
If you start like in the image I provided, the lawnmower and box should end up the other way around of what you posted. Counting from the top left of the island, the lava just on the island corner being (1, 1). When you first get the lawnmower on (4, 4), push it down a single tile to set up for the end. I hope that helps!
! Full solution spoilers for level V!
↑↑←↑↑↑←↓←↓→→→↓→↓→→↑↑↑↑←←↓↓→←←↓↓→→→↑↑↑→↑←←→↓↓↓↓←←↑←↑→↓↓→→↑↑↑↑←↑←↓↓↑→→↓↓↓↓←←←↑↑→↑↑→→→↓↓←←←↓↓←←←←↑↑↑→→↓→↓→↓→→↑↑↑↑←←↓↓↓↑→→↓↓←←←↓←↑→↑↑←←→→↓↓←←←↑↑↑←↑→→↓↓→→↓↓←↑→↑←←↑↑↑→↓↓←←←↓→→→↓→↓→→→↑↑↑↑←←↓↓↓↑→→↓↓←←←←←→↑↑→→→←↑↑→→↓↓↓
Push the lawnmower up, then push it right with the box until you can push the box down. Push the box down one, then push the lawnmower around the rock until you have gotten all the grass in the topmost row. Then push the rock into the gap between rock and lava on the right. Push the lawnmower down until next to the rock and push it right. Now the right side should be fully cleared and you can push the lawnmower left with the rock.
Push it left until the lawnmower is on the grass diagonally up right from the left lava pocket. Push the lawnmower down one. Push the box below the lawnmower and push the lawnmower up one. Push the lawnmower around the ring on the left until it is in the top right corner of it. Put the box in place above the lava on the left. Push the lawnmower down two until next to the box, then you can push the lawnmower right until it is ligned up with the remaining grass and the solution should be visible at this point.