$5k / month definitely does not get you a nice 4 bedroom in Palo Alto. Maybe in East Palo Alto, but that is a very different place in terms of quality of life, safety, and schools.

Edit: I decided to check, and there is one place in Palo Alto right now with 4 bedrooms at that price https://sfbay.craigslist.org/search/pen/apa?nh=83&max_price=...

From personal experience, as someone who was priced out of Palo Alto this year, it is rare to see a place at that price point in Palo Alto proper, and they tend to be quite run down. The one place available right now is actually in a good location and doesn't look too bad inside, so that's not a bad deal for the location.

On the other hand, you can get a great place in Seattle with views for over $1000 cheaper: https://seattle.craigslist.org/see/apa/5723972635.html