What does "court" mean in this case?

"A nervous man thrust a bouquet of flowers at a woman he's courting"

there are 5 definitions from the dictionary which have similar meanings and I'm thinking it's definition #5.

1 to try to please somebody in order to get something you want, especially the support of a person, an organization, etc.

2 to try to obtain something

3 to do something that might result in something unpleasant happening

4 if a man courts a woman, he spends time with her and tries to make her love him, so that they can get married

5 to have a romantic relationship before getting married




Thanks so much.