The following array formula returns the first entry in column B where it is not null and also where column A has cell value aaaaa.
= IFERROR(INDEX(B1:B6,MATCH(1,(A1:A6="aaaaa")*(B1:B6<>"null"),0)),"no match")
Note this is an array formula, so you must press Ctrl+Shift+Enter on the keyboard after typing the formula rather than just pressing Enter.
To return a similar result except for bbbbb, just replace aaaaa in the above formula with bbbbb.
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solved EXCEL – Search formula with multiple criteria