"About the macOS High Sierra 10.13.5 Update
This update is recommended for all macOS High Sierra users.

The macOS High Sierra 10.13.5 Update improves the stability, performance, and security of your Mac, and is recommended for all users.

This update adds support for Messages in iCloud, which lets you store messages with their attachments in iCloud and free up space on your Mac. To enable Messages in iCloud, go to Preferences in Messages, click Accounts, then select "Enable Messages in iCloud."

Enterprise content:
Variables used in SCEP payloads now expand properly.
Configuration profiles containing a Wi-Fi payload and SCEP payload install as expected when the KeyIsExtractable key of the SCEP payload is set to false."

(See below for article on security fixes in this update.)

Download pages for macOS 10.13.5 & Security Update 2018-003 updates:
(at post time download pages had incorrect Mar. 29th date, later corrected to June 1st.)

• Download macOS High Sierra 10.13.5 Update
  
  
• Download macOS High Sierra 10.13.5 Combo Update
  
  
• Download Security Update 2018-003 (Sierra)
  (Download page date changed to June 3rd.)
  
  
• Download Security Update 2018-003 (El Capitan)

Related Apple Articles:

• About the macOS High Sierra 10.13.5 Update
  
  
• About the security content of macOS High Sierra 10.13.5, Security Update 2018-003 Sierra, Security Update 2018-003 El Capitan (Info revised again June 22.)
  
  
• About the security content of Safari 11.1.1 (Info revised June 15th.)
  (available OS X El Capitan 10.11.6, macOS Sierra 10.12.6, & macOS High Sierra 10.13.4)

If you're running Security/AV software on your Mac, it may interfere with updates. Of course backup your current boot drive before updating. (And a bootable clone is a plus.)

FYI on Nvidia Web Driver Updates:
Users of Nvidia's web drivers should know that new OS updates (versions or later build numbers after Security Updates) break any currently installed Nvidia web graphics driver. I'd switch to the default Apple driver and reboot before updating, if your card is supported with the default drivers. If not, wait for a Nvidia driver update. (Some non-Mac EFI cards are not supported by default OS X drivers.)
Of course have a current backup (and if possible, a Clone) of your boot drive before any update. (As usual, I'll post download pages for Nvidia updates when spotted in the news and video topics page.)

Nvidia Web Graphics Drivers Update:
See this page for info/downloads of new Nvidia graphics driver updates for macOS 10.13.5 (17F77) and the new builds of macOS 10.12.6 and OS X 10.11.6 after installing Security Update 2018-003. (Updated July 9th to note new CUDA 396.148 release for macOS High Sierra.)