Is it okay for a 22 year old to hangout with a 17 year old girl?

I shifted major trice, first I was in premed but I failed to maintain my gpa, so I transferred to an art school, but I saw most of our graduates struggling as "starving artists" and I'm talking about the good ones, which made me shift into a more corporate degree to secure my finances.

So, I had to take first year credits again. My peers are nice, but as usual at times I get really insecure, because I am the oldest. I did look young (asian), so most of my professors and peers never really noticed until I say my age.

There was this girl in most of my class, she seems really mature and pristine. I took notice of her since the last term but I thought she would never talk to me. We smile at each other in the hallway, and later on turned to "hellos". Sometimes, when we get specially mentioned in class for excellence, we congratulate each other.

Then one time, the only chair available was beside her, so I sat there and was figuring out how to start a conversation when she suddenly asked me about my interests in tv shows.. and then literature and it went on and on. We laughed all over the place and thrown highfives (tho her highfive was more of a touch and squeeze five). Turned out she's as much of a geek as I am. I told her about these eccentric places I go to alone, because none of my friends are interested, and she said "Now you have someone to go with you." We talked hours til our class was dismissed. So, we said goodbye too many times it started to sound awkward.

She asked me to send her the stuff I told her about when we were talking, and I did as soon as I got home but I thought that maybe I seemed "desperate". She replied but I didn't know if I should continue it.

Today, we didn't talk about it. She didn't talk to me. Until, the dismissal. And she only smiled at me and said "Bye, (my name)" and that was it.
Is it okay for a 22 year old to hangout with a 17 year old girl?
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