My hosting company (OVH.com) is very cautious and does not push me into upgrading silently PHP on the servers. But I was still in PHP5 when I noticed that I could go up to PHP7.
WordPress informs me that the simple upgrade could improve speed by a ratio of 2x to 3x. So, it was easy to try.
Apart from an old plug-in which appeared unable to tolerate PHP7 (and that I was no longer using), the upgrade went well: I recommend the enormous speed increase for the web sites. This will be positive for my Page Rank in Google, for sure.