so by that point saying no to her caused an almighty meltdown
Not the point I know but you really can't give in to a 5 year old because they don't like the word no! You're gonna cause real problems for yourselves in the future and now in fact if:
You don't say and stick to the word no
You let a 5 year old play you off against each other!
This isn't about pizza this is about him undermining you as a parent. You both need to be on the same page re any disciplinary matters
Dd was hungry and asked to have it early
Wow! Sounds like you may be letting dd run the family/house! THAT needs nipped in the bud but quick!
My dd an adult now, if she had spoken to me like that she'd have been sent straight to bed and I'd have expected a sincere apology once she calmed down/the next day. Totally unacceptable behaviour.
Are you also going to bed very early with said 5 yo?! You've said no but I have to say I'm not entirely convinced given the original wording and other comments.
You're also all far too precious about leftover pasta! Perfectly acceptable and safe to eat the following day, cold or reheated even "zhuzhed up" with maybe some extra grated cheese, herbs etc
Sounds like they both take turns to go to bed at the same time as dd every night. So uve a feeling the 5yo regularly gets their own way. Absolutely! It's ludicrous!
pasta is vile the next day-in our house at least-dry and awful-no one will eat it
Am I the only one wondering how on earth op makes pasta?! 
Exactly that, I’d we waited for Dh to get home and cook we’d be waiting a long time, my child would be hungry, plus he can’t cook
As several have suggested the child could eat earlier alone, or she could have a more substantial but healthy snack to tide her over until dinner time. As a Scot I was raised we got soup and bread when we got home from school maybe salad/sandwich in summer and I did the same with my dd sometimes although I was mostly a lone parent.
There's a lot of miscommunication, lack of agreement on how to parent and allowing a 5 yo to rule the roost here!
This needs a serious sort out - pizza and pasta fussiness aside.
He can't cook? I'd say time he learned now he's a father! How's he going to manage if you are ever incapacitated or worse? It's a basic life skill! Perhaps he can learn alongside your daughter she's actually old enough to start learning too, including the fact that it's not on to waste food, financially or environmentally.