This is what I don't really understand - is it not as simple as plugging the MacBook into a monitor using an HDMI cable or something similar?
Yes, mostly using a suitable HDMI is all that is needed. But:
1. It was pointed out earlier that the 2011 MBP does not support 5K - only 2560x1600 pixels.
2. The 2016 MBP supports 5K, so should work fine so long as it is running macOS 12.3 or later.
3. The Studio Display is more than just a monitor. To get value from it, you need to use a Thunderbolt 3 connection.
The Mac and macOS system requirements (for the Studio Display) are "macOS Monterey 12.3 or later and Mac Pro (2019 or later), 13-inch MacBook Pro (2016 or later), 14-inch MacBook Pro (2021), 15-inch MacBook Pro (2016 or later), 16-inch MacBook Pro (2019 or later), MacBook Air (2018 or later), 21.5-inch iMac (2017 or later), 24-inch iMac (2021), 27-inch iMac (2017 or later), iMac Pro (2017), Mac mini (2018 or later), or Mac Studio (2022), iPadOS 15.4 or later and iPad Pro 12.9-inch (3rd generation or later), iPad Pro 11-inch, iPad Air (5th generation)"