Never use more than three fonts in a design. In fact, stick to two if you can. As most font families have a regular, bold and italic variation, there is simply no need to use any more.
Two key points of good type design are readability and consistency. However, using too many fonts will simply overwhelm the reader.
The editorial page above only uses two fonts, Playfair Display and Roboto. However as pointed out in the graphic below, each font has more than one variation. This provides the reader with just enough variety to keep reading but not so much where it becomes distracting.
