If you stopped doing any house cleaning, washing dishes and tidying up, how long would take for your place to look like a 'disaster area'?

Depends on when the Grandkids come over. But 1 week. 

4-5 days.

Less than 5 minutes after a cat woke up.  These guys can somehow get half the cat litter from the litter box and spread it ALL over the house (furniture, floor, carpet, bed, kitchen), shed enough fur to make a whole other whole cat, and deposit a pile of hairballs, puke, and/or turds somewhere in the house ... all in just 5 minutes!

About a week or so.

Depends.
Which "disaster" are we talking?

Honestly, since I spend so little time home ... it could go for a month or two before it would be noticeable.