I hope this is readable. Obiously merges with 5 are best. But in the puzzles you have chain reactions and for home you can deactivate those.

Read notation from right to left. So starting with 5 yields 2 better level and 0 starting level. Since for 6 and 7 you effectifly loose a starting item, those are worse. With no chaining you get the optimal output with multiples of 5. 20 looks interesting, probably bc 20 yields 8 with one lvl higher and 8 yield 2+1 level higher, thus having 3 to get to new level. Any higher item # is really tedious to get the number of items right.

# Chained Only 5er Home - no Chain
3 1.0 3 1.0
4 1.1 4 1.1
5 2.0 2-0 2.0
6 2.0 2-1 2.0
7 2.1 2-2 2.1
8 1.0.0 2-3 3.0
9 1.0.0 2-4 3.0
10 1.1.0 4-0 4.0
11 1.1.0 4-1 4.0
12 1.1.1 4-2 4.1
13 2.0.0 4-3 5.0
14 2.0.0 4-4
15 2.0.0 2-1-0
16 2.0.0 2-1-1
17 2.0.1 2-1-2
18 2.1.0 2-1-3
19 2.1.0 2-1-4
20 1.0.0.0 2-3-0