You can always pull them out and see if there's any location that looks dry. Practice removing and installing tires is great for if you flat on raceday anyway. I'd think they're fine though

Back in the day people used to age tubulars, but it wasn't for half a decade. Rubber does deteriorate with age, but I think a lot of that is due to UV light exposure. I would check the sidewall of the tires for any signs of cracking and check if the rubber seems particularly stiff or hard compared to a ne tire. If all looks good give them a spin and not worry about it/

I agree with the above. I would do it not only to make sure everything is good, but also to make sure you remember how to change out a flat, preferably efficiently and quickly, and that your on-road flat kit works.

It's surprising how easy it is to forget a critical flat kit item. Like valve extender remover tool, or even the right length tube (long-stem tubes don't fit in disc wheels, you need short 42mm stems) etc.

One really helpful tool for training flat kits at least, I've found, is a tire-bead jack. There's a small one, the "EZ Clincher" that actually is small and works as advertised (youtube has a review of it), or bringin the entire Kool stop tire bead jack if you can fit it somehwere. I don't bring them on races as I can get my tires on mostly without them, but for training, they make things a lot faster in the remount.

I would get a new pair of Continental Grand Prix 5000 clincher tires and latex tubes.

I’ve had the same latex tubes in my race wheels for over a decade….no issues.

A few days before the first race of the season I pump them up just to make sure they are ok, but have never had an issue. The inside of a tire/rim is a fairly protective environment.

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Even if the tubes are OK, "modern" tubes, latex/TPU is what I was thinking as well. The ride quality can be day/night.