Based on the context of the conversation and the typical uses of prepositions of place, here are the suitable answers to fill in the blanks:

1. **on**
2. **in**
3. **on**
4. **under**
5. **between**

So the completed conversation would look like this:

Mi and her parents are in the living room.
Mum: Do you know where our cat is?
Mi: I think it's (1) **on** the dining table.
(2) **in** the kitchen.
Mum: Do you see my book anywhere, sweetie?
Mi: Yes, Mum. It's (3) **on** the table. I saw it this morning.
Mum: Thanks, sweetie. Oh, I have to find my hat!
Mum goes to the kitchen.
Mum: Is it there? It's (4) **under** your book.
Mum: Do you need your book now?
Mi: Yes, Mum. Thank you.
Dad (from the living room): Honey, do you see my reading glasses on the dining table?
Mum: Yes, honey. They are (5) **between** Mi's book and the vase.