Will Ubuntu 16.04 LTS have an update for kernel version 4.5.2? I have an AMD GPU installed, and I heard this would fix AMD driver problems.
Ubuntu 16.04 will never have a 4.5.2 kernel update.
Ubuntu does not update with mainline kernel versions.
Canonical Kernel Team backports bug fixes and some support of new hardware from upstream kernels to Ubuntu kernels.
Important fixes get into Ubuntu kernels 4.4.0-xx from 4.4, 4.5, etc mainline kernels.
You can see the source of Ubuntu 16.04 kernel HERE.
It is possible that the fix you need has been already backported.
No, Ubuntu 16.04 will not have version 4.5.2 of the kernel. As you can see from a picture (taken from 16.04.x Ubuntu Kernel Support) of the kernel timeline for Ubuntu 16.04 below, the next version of the kernel will be a fork of version 4.8 of the mainline Linux kernel.