$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.
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.
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