You should start by reading the Subversion release notes for each version whose features you’ll be getting (1.5, 1.6, 1.7, 1.8):
https://subversion.apache.org/docs/release-notes/1.5.html
https://subversion.apache.org/docs/release-notes/1.6.html
https://subversion.apache.org/docs/release-notes/1.7.html
https://subversion.apache.org/docs/release-notes/1.8.html
If you don’t want to read each one in its entirety, at least read the Compatibility Concerns section, which will tell you about the new features in that version and what you have to do to enable them. You can weigh your desire to use each new feature against the inconvenience of performing the prerequisite steps. For example, representation sharing, which was introduced in 1.6, may save you significant disk space if you use a lot of branches, but if I remember correctly, you have to dump and load your repository to get it. If you’re less concerned about disk usage and more interested in not incurring downtime during such an upgrade, you might choose to forgo this feature.
In order to actually install the new versions of Subversion and Apache, you would follow whatever steps you originally used to install the old versions. Perhaps you used whatever package manager is commonly used on your operating system; I can’t advise you with regard to that.
