How can I work out the BTU rating of my AC when I can't get to the indoor unit?

The outdoor unit label is all you need. The model number there will get you the capacity, and in most cases the capacity is actualy baked into the model number itself. Look for a two digit number in it, like 09, 12, 18 or 24, wich usally stands for thousands of BTU. So a model with 18 in it is most likely an 18,000 BTU unit. If there is no obvious number, just type the full model number plus the word 'specifications' into a search engine and the manufacturer's datasheet will come up with the cooling capacity listed in BTU or kilowatts. One kilowatt is about 3,400 BTU if the sheet only shows kW. The outdoor unit and indoor unit in a split system are sold as a matched pair, so the outdoor label tells you the whole system's rating. No need to climb up to the indoor unit at all. I went thru exactly this a couple of years ago because our indoor sticker had faded in the sun and the outdoor one was easy to read from the ground. Photo of the plate, quick search, done in five minutes. As for working backwards from the power input, you can get a rough idea. Modern units produce roughly three times the cooling compared to the electrical power they draw. So if the label says 1,000 watts input, you are looking at somethig around 9,000 to 10,000 BTU. It is only a ballpark because it varies with efficiency, but it is close enough to spot an undersized unit. For your room, 5 by 4 metres is 20 square metres, and the common rule of thumb is around 500 BTU per square metre for a lounge with normal ceilings. That puts you near 10,000 BTU, maybe a bit more if that afternoon sun hits the room hard through windows. So if your search turns up an 18,000 BTU unit you are definately not undersized, but if it turns out to be a 7,000 or 9,000, that whould explain the struggle on hot afternoons.

One thing I'd check before writing the unit off as undersized, is it actually blowing cold? Ours was rubbish on hot afternoons and I was convinced it was too small, but the filters were absolutely choked with dust. Gave them a wash, airflow was way better and the room cooled fine after that. Same with the outdoor coil, mine was grimy and that kills performance too. If the model number turns out to be a 9 or 12k unit it might still be worth a clean before you go shopping for a bigger system.

One thing I'd add about the datasheet figures, and this trips a lot of people up, is that the capacity printed on them is usually quoted at a standard test condition around 35 degrees outside. On a 40 degree afternoon the actual output drops noticeably, so a unit that looks adequate on paper can still fall behind in a heatwave, which matches your symptom of the room struggling after lunch. Also check wether the outdoor label lists a rated and a maximum capacity, because some manufacturers quote the maximum in bold marketing and the rated figure in small print.