V.

$\text{1.}$ They probably will build a big house, but it isn't sure at all.

$\text{→}$ probably ⇒ TLD

$\text{2.}$ I promise I won't be late for school.

$\text{→}$ promise ⇒ TLD

$\text{→}$ be late for school: muộn học

$\text{3.}$ She went to the gym yesterday afternoon, and she probably will go there this afternoon, too.

$\text{→}$ yesterday afternoon ⇒ QKD

$\text{4.}$ I guess it will cost a lot if you buy furniture for your house.

$\text{→}$ Câu điều kiện loại 1: S + will/ can/ may + V<infi> + if + HTD

$\text{→}$ buy sth for sb/ sth: mua cái gì cho ai

$\text{5.}$ Robots might do housework in the future.

$\text{→}$ might + V<infi>