Alternative way to list :
In the first case, if she had 1 more plum, then she would have 5 remaining plums, which can be divided equally among the 5 friends.
So, (number of plums she has) + 1 = a multiple of 5.
Which means that : Number of plums she has = (a multiple of 5) - 1
Likewise, in the second case, if she had 1 more plum, then she would have 9 remaining plums, which can be divided equally among the 9 friends.
So, (number of plums she has) + 1 = a multiple of 9.
Which means that : Number of plums she has = (a multiple of 9) - 1
So, list multiples of 5 and 9. Then subtract 1.
5,10,15,20,25,30,35,40,45,50,55,...
4,9,14,19,24,29,34,39,44,49,54,...
And
9,18,27,36,45,54,63,72,81,...
8,17,26,35,44,53,68,71,80,...
We also get the same least number of 44 plums.