In this case, your husband is not behaving like a mature adult, or how a good parent should behave towards a child. Your stand on the issue - to interfere on the part of your daughter - is not only correct, but your responsibility as a loving and concerned parent.
It sounds like your husband values being a playful guy, which is fine if the child's feelings are taken into account. But because it's always fun for him, he can't seem to understand that it's not always fun for everyone. It also seems that he takes the rejection of it personally, and blame-shifts onto a 5 year old ("...he should be able to do as he pleases in his own home and she should get over it.")
He says sometimes she doesn't mind him doing it, and how is he supposed to know if she'll get upset or not.
By reading her body language. If he gets into a crouch position and she smiles or laughs, it's fine to move forward. If she looks tired, frightened or tense, it's not. If he's unsure, wait a while until she seems relaxed.
This is what your child will learn/is learning from his behavior: his feelings matter more than hers. It might even go as far as her feelings don't matter. As kids tend to think the world revolves around them, when something is wrong, they tend to blame themselves; they tend to experience negativity/criticism not as a reflection on a discrete character trait (e.g. bravery/perseverance/resilience) but on their inherent "goodness". This self-blame can develop into low self-esteem and problems later in life, especially if it's frequent and across several or more aspects.
A well known example similar to this is tickling. There is welcome, loving tickling and there is abusive tickling. Adults like to tickle kids because we like to hear their laughter, and interpret their laughter as joy. Kids enjoy the attention of their parents, the physical contact, the roughhousing, and the sensation of being tickled to a point. At some point, tickling becomes uncomfortable. It becomes so uncomfortable that it was used through the ages in different cultures as a form of punishment/torture on adults. Most parents are aware of abusive tickling and give the child some power in this very unequal dynamic: stops to check in with the child, and a safety word, or "Stop", which is consistently respected by "the tickle monster".
Perhaps this is how your husband was raised, so it's his default setting, or he may be lacking the empathy needed to see this issue from your daughter's perspective. Either way, it will damage his relationship with his daughter to some degree.*
It may be that this is the only situation in which your daughter's feelings are disregarded. If so, repeated explanations that what she feels, no matter if he thinks it's appropriate or not, is as valid as his own feelings, and if he values having his feelings taken into consideration, so will his daughter, even (maybe especially) at the tender age of 5 may do the job. If you see other evidence of this lack of empathy with your child, he may need a third party to intervene: her physician, your pastor, or someone else whose opinion he respects, even a family therapist if his dismissal of her feelings is across much of the board.
Edited to add: In light of your husband's difficult childhood, he may be overly focused on bringing joy to your daughter's life, something he himself missed out on. It doesn't change anything in the answer, but I would add an explanation to your husband that joy can be experienced in ways not expressed by laughter, and laughter does not always mean joy (see tickling.) He's not failing to bring joy by failing to make her laugh. Respecting her feelings and making home a safe haven for her may bring her a serenity/happiness he also missed out on as a child. Ask him to picture how he would have felt if his parents cared about/were attentive to/respected his feelings as a child. That might be helpful. (Joy elicits a feel-good reaction in your husband because he can see it and he is rewarded as well for it. Happiness/serenity isn't as visible, and doesn't bring on the same experience, but is just as important for her well-being.)
Have you ever asked him exactly how she should go about "getting over it"? What are the steps she should take? If he can't come up with a better plan than "she just should", seeing how this is not a reasonable expectation may be helpful.
*When I was a child, my father used to tickle us mercilessly, ignoring our cries to cry to stop until the laughter turned to sobbing, at which point he would get angry and walk away while muttering criticisms at the tearful victim. It was awful, and I hated it. He disregarded our feelings in many many ways, and I had a very tenuous relationship with him as an adult. What I didn't realize until decades later was that my father lacked empathy to a degree which was pathological. He just didn't understand on a deep emotional level that what he thought/felt/believed wasn't what everybody thought/felt/believed (or should have done so.)
6 Ways Childhood Abuse and Neglect Leads to Self-Blame in Adulthood