Caltech is located in the state of California.

5.0 is good for caltech.

Athenaeum at Caltech was created in 1930.

CalTech-- officially known as California Institute of Technology-- is located in Pasadena, California.

Harvard and Caltech.

I completely disagree.

Caltech may be in the top ten engineering schools but certainly not top five...while Harvard is not even in the top ten.

The best answer is Stanford and UC Berkeley.

That depends how you interpret "rival". From a ranking/academic perspective, you may be right (though I feel Caltech is comparable to MIT). From a personal/historic perspective, MIT has a long history of hacking with Caltech and Harvard (MIT stole the caltech cannon!). In the MIT student culture, Caltech and Harvard are ingrained as the main rivals.