난 이 회사를 5년전에 인수했다. = I took over this company five years ago.

=> Another way: Your sentence is okay and this is another way of saying it.

I bought this company five years ago.​

우리는 5명의 관리자를 고용할 거야. = We're going to hire five managers.

=> Another way: Your sentence is okay and this is another way of saying it.​

We will hire five managers.​

우리는 배경조사는 = We're looking at the background.

​=> Your sentence has a correct grammatical structure, but this has the correct usage/ expression.

​We're looking for a background check.

​Thank you, Eunchan~