First use of Vulkan API with Intel HD Graphics 5000

Hello,
I am currently trying to use Vulakn Api on my Mac OS but when the result of the vkCreateInstance(...) is VK_ERROR_INCOMPATIBLE_DRIVER.

I have create a custom VkApplicationInfo :

    VkApplicationInfo vkAppInfo    = {};
    vkAppInfo.sType                = VK_STRUCTURE_TYPE_APPLICATION_INFO;
    vkAppInfo.pApplicationName     = "app";
    vkAppInfo.applicationVersion     = VK_MAKE_VERSION(1, 0, 0);
    vkAppInfo.pEngineName           = "No Engine"; //TODO plus tard
    vkAppInfo.engineVersion           = VK_MAKE_VERSION(1, 0, 0);
    vkAppInfo.apiVersion                 = VK_API_VERSION_1_0;

I thought it’s maybe because my graphic card is too old, I have a Intel HD Graphics 5000 1536 Mo.

Does the result of vkCreateInstance(...) is because of my graphic card ?

You can check https://vulkan.gpuinfo.org/ for hardware support - on a quick glance I don’t see your GPU in there.
However, if you are on macOS (as opposed to e.g. running a different OS on the hardware) you cannot access Vulkan directly because it is not supported by the OS. You can use MoltenVK (which is part of the Vulkan SDK, so you may already have it), a translation layer that turns Vulkan API calls into corresponding Metal API calls.