I know many families have both a first night seder and a second night seder with a separate set of guests. How flexible is this? If a family has travel constraints, could they just have a 5th night seder, while following the other laws for the whole period?
Halacha requires that one have a seder with certain elements on the evening of Pesach, meaning the first night (and second in the diaspora). An article from Aish HaTorah lists the mitzvot that are obligatory then:
There are actually seven different mitzvot that we perform at the Seder. Two are from the Torah:
1) telling the Exodus story 2) eating matzah
The other mitzvot are rabbinical:
3) eating Marror (bitter herbs)
4) eating the Afikomen (an extra piece of matzah for dessert as a reminder of the Passover offering)
5) saying Hallel (Psalms of praise)
6) drinking the Four Cups of wine
7) demonstrating acts of freedom and aristocracy ― e.g. sitting with a pillow cushion and leaning as we eat and drink, and beginning the meal "with a dip."
A guide from Star-K includes more details (with citations) of the halacha, including timing. All of this takes as given that you will hold the seder on that night; the timing details are about how early or late you can do things, not about deferring to another day.
Now, there's nothing that says your seder needs to be a big, elaborate thing. I've heard of people who couldn't go to a larger family gathering who just made a small one at home with just a couple people. If your family can't gather until later, don't skip the obligations of the first night(s) -- do something then, and if you want to do something else later, you can.
However, if you're holding a seder-like gathering other than on the first night(s), you need to be careful to avoid making blessings in vain. The fifth night of Pesach isn't yom tov, so making kiddush then would be inappropriate. Similarly, some of the other b'rachot refer to obligations that you will not actually have on that night. Consult your rabbi for what specific changes you need to make. But since the main point of the seder is to tell the story, you can still have a meaningful gathering even if it's not actually a seder.