You can do it even without slots:
Map[Map[Flatten @* List] @* FoldList[List]] @ test
{{{4}, {4, 2}, {4, 2, 2}}, {{9}, {9, 1}, {9, 1, 5}}, {{5}, {5, 2}, {5, 2, 9}, {5, 2, 9, 3}}, {{5}, {5, 2}, {5, 2, 7}, {5, 2, 7, 1}, {5, 2, 7, 1, 1}}}
Also
Map[Extract[#, Map[List] @ Range @ Range @ Length @ #] &] @ test
{{{4}, {4, 2}, {4, 2, 2}}, {{9}, {9, 1}, {9, 1, 5}}, {{5}, {5, 2}, {5, 2, 9}, {5, 2, 9, 3}}, {{5}, {5, 2}, {5, 2, 7}, {5, 2, 7, 1}, {5, 2, 7, 1, 1}}}