I completely understand Make.
My DD is 4 now, and my XP picks her up and drops her whenever it suits him. He has made lots of noise, but has never put DD and her needs first, it's always been about him.
I understand the concept that DC deserve to have a relationship with their father, but at what cost I find myself asking.
I have been to court twice, I have residency, he has PR, as do I, yet he has done whatever he can to avoid paying maintenance and we are now left with a court ordered contact order that he just doesn't stick to.
There is no way of making him stick to it if he doesn't feel like it.
The result....I have a 4 year old DD who adores him and has slowly and systematically had her little heart broken, over and over and over.
There is not a court in the land that will make him see DD, there is not a police officer in the land who will force him to turn up for DD.
If I had my time again, I would cut him off before DD knew him. I wouldn't have let her build a relationship with him, only to be let down so badly so many times, and the only one who bears any consequences are DD, and to a much lesser extent, myself.
Your DD is 5 months old, who she doesn't know, her heart can't grieve over. 
I have bent myself into a pretzel shape over the years to facilitate contact, yet XP still only sees her when he feels like it. Months and months can go by before he even bothers texting or ringing me to arrange contact, and there are absolutely no consequences for him, none whatsoever.
Don't find yourself in my shoes in a few years time, not knowing what to say to console your DD as to why her daddy hasn't bothered again, knowing nothing you say can heal her pain. 