He called me " baby" for the first time? We communicate 5 months already. Why he did that? He also wrote to me on Valentine' s day. Why?

It looks like casual flirting. Unless he is extremely shy and insecure, he doesn't have "plans" behind that and that is not a way to test the waters, but that is just what it is: he called you baby, and wrote you on Valentine's. If you take those things alone without seeing a bigger hidden plan behind, that is just very casual, light flirting.
In comments you say you have sex with him and he cuddles and stuff so he is just getting the benefits of the full passion but without strings attached, so it sound coherent to say "baby" and small flirts like that.
Signs of wanting a relationship should be more concrete if that is what you're trying to investigate, such as trying to spend more alone-time with you that is not related to sex (or that doesn't lead to sex in the night), trying to know you better and trying to become a fundamental part of your daily life by asking many questions and finding occasions to help you about a lot of things, trying to get to know your friends and family and viceversa, communicating often on chats about personal topics, being affective (saying cute cuddly things etc), making you feel important for your presence in his life and how this makes him feel more complete, etc etc.
All these things are signs of romance, if there is nothing of this it's clear he is only interested in sex and passion, nothing more.
Nothing meaningful I guess, really wait for concrete, real, direct signals of romance to conclude he is interested in a relationship, otherwise you trap yourself into trying to see things where there aren't and building fantasies and plans upon the nothing...
Also in case you are into him and want a relationship you should ask him to become exclusive and official, and if he refuses you should move on and focus on other guys instead, otherwise he'd keep using you as a fuck buddy and you'd keep dreaming and be not satisfied with the whole thing.
Maybe he just talked with his bff about great sex he has with you without needing a relationship and he was like "oh wow maybe I could flirt with her too then" and decided to keep an eye in case you stop seeing your friends with benefits.
Especially if you never talked with him personally and didn't exchange contacts directly.
It seems like he is growing fond of you. Apparently, the more he gets to know you the more he likes you. It seems like he see a long-term relationship possibility here. This seems like a positive thing.
He's ready to take relationship to the next level.
My current... girlfriend... started calling me baby after the first week, which was way too soon, but whatever.
5 months is about right
That's weird. Could be a sexual thing.
Like, "Hey baby 😉"
Huh... well any other ideas I throw out would be pure conjecture. I'm sorry
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Maybe he likes you and is getting closer.
Seems he likes u
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