Of course your'e right in thinking his actions are not in the best interests of your child, they're not, you don't have to be Dr Phil to come up with that glaringly obvious conclusion. However, Letsadmitit and Sgb talk a whole lot of sense, this is definitely a pick your battles moment. If this were to go to court, the judge would view the loss/ disruption of contact a greater negative impact on your DD than her father's selfish and ill judged need to create another "happy" family. As hard as it is doing the opposite of what your gut says, this is one of those rare occasions where you should do just that.
You'd be amazed what five year olds and even younger kids can absorb (heartbreaking as it is that they should even have to). Invest your energies and emotions where they will get their best return, which is supporting your DD and her kick-ass mum. You are the greatest influence in your DD's life right now, she will be looking to you to validate her feelings (a bit like when kids hurt themselves and they judge their own response by looking at our reactions). Of course she's confused, its confusing!
I can't imagine the hell this man has put you and your children through and just when there appears to be a plateauing of the awfulness he goes and raises the bar, the fucker. However, this isn't about his demands (when will these fuckers realise its not about their rights, its about their responsibilities) or your pain (as devastating as that is), this is about a little girl and her rights and our responsibility as mothers to be our children's advocates. She's only 5, even if she wasn't exposed to these confusing circumstances, it would be hard for her to articulate her feelings. If she had/ has a good relationship with her father prior to your separation you can safely assume she would want this to continue.
Just be there for her; absorb her anger, listen to her fears and worries and reassure her that you aren't going anywhere. Most importantly, there is nothing she did or said, didn't do or didn't say that caused this (my counsellor says that children often assume responsibility for the negative actions of the adults around them).
Disengage, disengage, disengage. Easy for me say, just when I think my Ex's shit no longer effects me, he goes and pushes the only button he has left (DD), disengaging is a process and one which you and your DD will benefit enormously from.
With all the shit my Ex has put me through (and he has put me and DD through A LOT of shit), the thing that still and probably will always hurt the most, is the need for me to support DD in managing the most basic expectations of her father.