Alternative way to install that could be easier (has a fairly recent version of Nginx):
$ sudo amazon-linux-extras list | grep nginx
38 nginx1=latest disabled [ =stable ]
$ sudo amazon-linux-extras enable nginx1
38 nginx1=latest enabled [ =stable ]
Now you can install:
$ sudo yum clean metadata
$ sudo yum -y install nginx
$ nginx -v
nginx version: nginx/1.16.1
