WOW....so many things...where to start...
1) small children have honest feelings and aren't very dishonest about them. If she is not comfortable around him, it may be that she is picking up on something that you don't. I would talk to her and ask her why she is shy around him. See if it is fear of something about him, worry that he will try and take her daddy's place, or simply that she doesn't feel that she knows him all that well. If it is cause her father said somethign to her, she will tell you at this time...
2) If your bf is "threatening" your relationship regardless of how long you two have been together, because your FIVE year old is having issues with your relationship then maybe you should let him walk. ANY man who makes you choose between him or your child is not worth your time of day. This is not a matter of respect, unless it is his disrespect of your concern over your daughter's reactions...or his disrespectful "threat" to you.
If you want to work this all out that is totally up to you, but you need to take a hard look at what is real and what is going on. Talk to your daughter and find out why she feels the way she does. Then talk to your BF and tell him to step off and deal...that your daughter is first and foremost in your life and you need to work this out with her. IF this is coming from her father, talk to him and tell him that while you appreciate his concern, all he is doing is causing confusion and pain for his daughter and he needs to knock it off. In the future he needs to bring up his concerns over your dating habits with you and NOT with your child...
Good Luck... ;-)