No interest.
I know it seems simple, but if you're just putting five people together, adding their scores, and declaring a winner, no one would care much about their team score. They'd still be looking at their own individual score and comparing it to others', especially if they were shooing the match with solos who weren't even on teams.
If you wanted to do teams where people cared, you would need a discrete team league with their own day to shoot and organize it something like other individual sports work their leagues, something like how dart leagues work. You could have 5 teams, and say something like it's a minimum of four players per match, and a maximum of 6, and at least two of your players on a given day need to be women. Then Stage 1, everyone runs it individually and scores are totaled based on Unlimited Scoring rules. Teams are awarded 4, 3, 2, or 1 point based on how they finished. Stage 2: Mixed doubles. Each team fields one 2-person squad, one male, one female. Total times for the squad based on Unlimited Scoring rules. Award points (1-4) to each team by comparing totals. Stage 3: Triples. Three person squads, minimum one woman per squad, LIMITED scoring rules. Stage 4: Doubles. At least one Marksman or Sharpshooter per squad. LIMITED scoring. ... and so on, and so on. That's how to make a
team aspect relevant. Mix up how each stage works, do NOT have everyone shooting every stage, and give the captain's role in squadding have a real impact on the outcome of the match.
As you described it, it seems like I'd be paying an extra $5/match, and in exchange, I lose the freedom to stay home when I don't feel like going, and once a year I probably don't get a trophy.
Another way to do a team is to just do one for a particular interest, and not try to make it part of the framework of any particular match. CZForum.com is a forum site like this one, but with MUCH MUCH less traffic. CZFirearms.us gets more traffic in an hour than CZForum gets some weeks. But CZForums actually has a CZForum shooting team. I don't know all the details of it, but at least two or three (maybe all of them, not sure) are in Florida. And they have team shirts and compete in events together. I've competed in events one or two of them were in. I met one of them briefly. Cool guy, and he was quite good. I don't think they're particularly formal. I think it's just a group of guys who created a team identity for fun, and they designed and had team shirts made. I suppose you might say their interest is to promote their own site and CZ firearms, in general. Personally, I think something like that would be awesome. Get together with four friends who shoot, and make team jerseys. You could come up with a funny, meaningless name, or you could even name your team to promote some local charity. Whatever. Just something to build your shirts around and create a team identity.
