Hi sidesshow_steve,
Welcome to the mattress forum:).
Congratulations on your latex mattress! 
and yes you are correct that latex is a very durable and can keep its qualities for decades.
Sorry about the back pain….coupled with it being really comfortable when you first fall asleep. As Bill was pointing out … In general, issues with “pain” earlier in the night tend to be surface comfort-related, but issues with “pain” in the morning tend to be more alignment (deep support) related, There will be a break-in and adjustment period for any new mattress or sleeping system as the mattress loses any of it’s “false firmness” and the cover stretches and loosens a little and also … the materials settle and your body gets used to a new sleeping surface that is different from what it is used to (see
post #3 here) and I’d be curious to know for how long you slept on the new mattress and your history with the previous one. Unfortunately, it would be difficult to pinpoint and give you any specific answers that would apply to specifically to you because there are too many interconnected variables and … “it depends” … suggestions that can help one person or even many people may be completely unsuitable for someone else because each person and set of circumstances are very different. There are some general guidelines as to what tends to cause back pain in post #2 here that you may find helpful.
A couple of questions, what latex mattress did you buy? Do you have any other information about the layers - height, formula, process, brand? And it’s 5 layers? This is important to give you any guidance on switching any of the layers, and how it may affect your support/pressure relief needs.
Post #2 here I mentioned above has some good information about the many different symptoms that people may experience on a mattress and some of the most common causes behind them.
Hope this helps a bit and once you provide a bit more information I’ll be happy to go into more detail.
Phoenix