Travel from Madrid to Santiago de Compostela

Five hours is plenty of time. Flights from the US often arrive early but even if they are a bit late, you will have time.

Look at Vueling in addition to Iberia.

I see 8:25 and 11:17 trains from Chamartin to Santiago, direct.

I'm pretty sure your train connection would be on Renfe, but there are other companies
that operate some of the train service in Spain, so double check, since you don't mention
your exact date of travel.

I suspect you know that there are some risks with the two ticket approach, but having
said that, to get in touch with Iberia, 1) if you are in a city that Iberia itself (not via
codeshare) serves, go to the airport 2) try calling them late at night US time/morning
Spain time. It's more likely your call will get routed to agents in Spain who will have
more experience trying to manage the change you are looking for.

Barajas is a big, big airport, so there will be a fair amount of walking to go between
arrival/baggage claim/checkin and back.

I think your inbound flight is on Iberia, but if it's on United or American, there will be
a terminal change that requires a bus ride. All this to say that 5 hours should be
fine if your flight is on time, but an inbound delay will eat away at your confidence
level.

If you want to take the train, you will have to manage your own transfer from the
airport to Chamartin, which is another time consumption factor.

Only Renfe serves Santiago.

Flying into MAD on Iberia, you will have to change terminals, but five hours is plenty of time. Yes, there are long distances but the signage is excellent in that airport. I would not worry at all.

Two years ago, my luggage was tagged only as far as MAD, not to XRY, which was my final destination. So I had to get my bag nd do the entire check-in process again, with only a 1 hour 50 minute connection. I was worried but it turned out the I had time to spare.

Last year, I had only 50 minutes to make my connection; to say I was nervous would be an understatement.

Not only did I make my flight, but I had time to stop in the lounge for a drink and wash.

I just checked Renfe again for April 16, 2026, 2 passengers, one-way, and it has direct trains leaving at 8:25 and another at 14:40. https://venta.renfe.com/vol/buscarTrenEnlaces.do?c=_Lp5D
As our flight arrives at 6:50 and we still have to collect our checked luggage and travel to Chamartin station, I'm not sure we'd be able to make the 8:25 train, though that would be the ideal.

My mother is from Galicia, Spain and I've been to Barajas airport several times though our connections were always booked on the same ticket, but this is the first time I've booked the flights on my own. I appreciate all the advice. Thank you!

This is my thought:

There is a decent chance that you could make the earlier train IF you take a taxi to Chamartin.
BUT there is also a chance that you will not, so I would book the later train if there is an option to change trains, even for a small fee. That's happened to me, but with IRYO. I had booked a train around 11am for Cordoba but I got to the airport so fast (taxi) that I was there in time for a much earlier train, and IRYO allowed me to switch for free. But they do not go to Santiago. See if RENFE has a changeable ticket.

I thought that there were other trains to Santiago, with one change..if that's true, why not take one of those?

Also look at the Vueling flights and see if those would offer any benefit time wise.

Where are you headed in Galicia...Santiago and anywhere else? We were there in June in the past two years, and I've just booked my hotels for a visit in September.