Only the current version of OS X and Pages are in the OS X App Store anywhere. Older versions of either are simply not made available by Apple.
You may have deliberately, or unintentionally installed software on your Mac that is creating these performance issues. I have used Pages v5 on Yosemite and El Capitan and it performs no worse across operating system upgrades. If you are opening large, image rich documents, or ones with scores of tables or shapes, then it will slow down. Reinstalling Pages v5.6.1 to solve a performance oriented problem is a waste of time.
For a potentially quick performance tweak, power off your Mac and then boot it into Safe Boot mode:
- On Power-on, press and hold the shift key until you observe the horizontal boot progress
- You will arrive at a full-screen login panel that in the upper right corner will show Safe Boot.
- After you type your password, but before you press the right-arrow to login, press and hold the shift key again until you see icons on your Desktop.
- Try Pages in Safe Boot mode. Does it work differently?
- Reboot normally.
Any improvements?