Pages not responding/wont open

Pages v5.6.2 is expected to run on El Capitan 10.11.6, not on Yosemite 10.10.5. That is your primary problem — incompatible application. Either restore Pages v5.5.3 from a Time Machine backup, and stay on Yosemite, or upgrade directly to Mojave 10.14 from a Mac App Store download. Hold that thought.

Although High Sierra 10.13.6 is still available in the Mac App Store, it may not allow you to download it to a machine (your 2013 MBP) that meets the Mojave hardware requirements.

The key factor is that you may have printer, scanner, or third-party applications that may not be supported on Mojave either yet, or ever, and that may require paid upgrades from third-party vendors. Consider these factors before choosing a macOS upgrade that can give you access to the current Pages, Numbers, or Keynote.

You can check with RoaringApps to see about Mojave compatibility with third-party applications, but as it was just released, it may not be as accurate as it will be later after more input from users. Always check the software vendor site for compatibility questions.

If you choose to upgrade macOS, I would recommend this approach:

1. Download the free Malwarebytes, and perform a malware sweep of your Mac. Many of us use this utility for routine checks. It is not an anti-virus tool, and will offer to remove any discovered malware. Good idea to run this regardless of upgrade plans. Requires OS X 10.9 or later.
2. For your printer, scanner, or other non-Apple applications, check the vendor sites for Mojave support. A product that says OS X 10.6+ or later is an insufficient answer. Drivers for printers/scanners last updated three years ago will likely not work.
3. Boot into Recovery mode (command+R) on fresh boot. Run Disk Utility : First Aid on your boot drive to verify all is well. Follow with a normal reboot.
4. Perform a final Time Machine backup.
5. Only if you are satisfied with step 2 that you have product support that justifies an upgrade, proceed with the Mojave upgrade by downloading from the Mac App Store. This upgrade will not wipe your drive, and your user data should not be effected at all.

What specific version of Pages (Pages : About Pages) are you using on Yosemite 10.10.5? Was this a Pages document you created yourself, or received from someone using a newer version of Pages?

What is “/Always Application?”

You now must have High SIerra (10.13) or later installed as a prerequisite for installation of Pages (v7.2) from the Mac App Store. Until you satisfy this criterion, you will not be able to download or install the current, and only Pages application from the Mac App Store.

Try pressing and holding down the shift-key while you launch Pages. Then double-click a random Pages document to see it will open normally.