Hi Lynn
Tim is quite correct in what he told you. Unlike Tim I arrived at T5 at 4.15 am for the 6.15 am flight figuring, rightly or wrongly, that as the first leg of the journey was to Madrid it would be classed as short haul.
The airport was practically empty at that time with just a handful of people, some of who must have been there all night as they were still sleeping, there were no check-in desks open. After wandering around thinking I was in the wrong place I was approached by a friendly staff member of T5 who asked if he could help me, I told him I was looking for where to check in for the flight to Madrid and was told "You can't check your baggage in until 5 am as the check-in desks don't open until then but you can get your boarding pass from one of the machines", he then helped me get my boarding pass. The airport began to spring into life around 4.30 am when people started to arrive.
I don't know what time the JY airport rep arrived, I personally didn't see her until after I had checked my case in at 5 am and I know a couple of people made a complaint to her about the lack of proper information in our holiday information pack.
Someone else on our trip had enquired the night before about the check-in time and was told it was 5 am. To avoid any confusion it might be an idea if you enquire with British Airways at T5 as to what the correct check-in time is, that way you will be sure, always assuming your flight time is the same as ours. We flew to Madrid with BA although our itinerary said Iberia, I know they are part of some alliance.
Have a great holiday, Costa Rica is beautiful, I am so glad I went while we still had the chance to go with JY.
Kind regards