“I'll take 5B.”
I'll take … announces a choice in shopping or house-hunting. Here it means deciding to rent apartment 5B. In other settings it can choose a purchase or a contract option.
B1-23 / CEFR B1 / EPISODE 23
Checking a lease and deciding to move in
SceneMr. Doyle is showing Tina apartment 5B. Sunlight fills the room. He has brought the lease and the keys.

WORDS & CONTEXT
I'll take … announces a choice in shopping or house-hunting. Here it means deciding to rent apartment 5B. In other settings it can choose a purchase or a contract option.
Cross something off a list means to strike it through because it is finished or no longer needed. The previous tenant already painted the kitchen pink, so Tina no longer needs to buy pink paint.