Error: Typescript Feature 1.5. Current language level is 1.4

It's a ReSharper setting. From the menu bar in Visual Studio, click Resharper → Options → Code Editing → TypeScript → Inspections, then change the TypeScript language level to the relevant value.

I found out how to fix this. First, if you are using Resharper, as others have mentioned, you need to indicate the version of typescript you are using:

However, within Visual Studio you need to go to Tools/Extensions and Updates and upgrade the Typescript extension to the latest version.

Do this by searching for "typescript" under the "installed" tab. In the yellow box I highlighted you should see a message saying that any available updates are available under the "Updates" tab. Go to the "Updates" tab and update your typescript extension to the latest version. (I had already made the update so no update selection is now available to me for Typescript).

UPDATE:
It is simplest to go to download and install "Typescript for Visual Studio" to get the latest version: https://www.microsoft.com/en-us/download/details.aspx?id=48593