Vulkan is a high performance, low-overhead, 3D API from Khronos. This should mean improved graphics with a lower CPU utilisation. Vulkan drivers shipped with Android Nougat firmware for select hardware, including the Snapdragon 810 chipset found in the Xperia Z5 series.
However, Sony has confirmed that the Xperia Z5 family does not have Vulkan driver support on Nougat firmware. The only Sony Xperia devices to support the Vulkan API are the Xperia X, X Compact, X Performance and the XZ. However, all is not lost for Xperia Z5 users as there is a mod on XDA which ports the Vulkan drivers which you can find here.