How can I extend my camera's battery life?

Just buy as many batteries as you need, plus a charger for all except the one currently in the camera. [When travelling by plane, you're not supposed to carry Li-ion batteries outside of their 'device'. I've checked with airlines that 'device' can include the charger.]
After comments This appears to not be an aviation authority rule, but one applied by airlines, who do have the final say in what they'll let you board with.

Squeezing a couple more shots out of a camera is really a futile endeavour.
Switching off live view, setting the camera to fall asleep sooner, not using the onboard flash - all these can help, but rather than constantly worrying about it, just get another couple of batteries.

Battery-life is affected by many factors, so the standard CIPA rating is designed to compare numbers easily but it has a specific procedure.

A DSLR like the D5600 is very efficient with battery-life and they are ways to get more out of it:

• Reduce Flash usage: Flash requires a lot of power and you can often almost double the number of shots per charge by simply not using it. Your photos will generally be better for it! Too often I see people with the flash permanently enabled and trying to photograph a building or the sky! Flash has limited reach and only serves to drain battery-life in those situations.
• Review images less frequently and for less long. The rear LCD of most cameras is a heavy consumer of battery-life. If you have automatic review turned on and want it on, there is usually an option to choose how long it stays on which you choose a shorter time. Don't remember exactly what options are on the D5600.
• Similarly to reviewing images, avoid using Live-View as it consumers even more energy since it must keep the rear LCD on and power to the sensor!
• Lower the brightness of the screen so that is consumes less power when you use it.
• Turn off Bluetooth. The D5600 does not use a Low-Energy variant so it used more power to keep Bluetooth on.

To extend your battery life while touring:

1. Use the viewfinder. Turn off LCD display.
2. If you must use the LCD display, reduce its brightness. Use LCD display as little as possible.
3. Turn off automatic review of each picture taken. Resist the temptation to check photos on camera LCD screen.
4. Use natural light. Minimize the use of flash.
5. Turn off the feature that lets your camera track focus on a subject. Don't let the camera keep focusing and refocusing on a subject. The lens motor takes up considerable power.
6. Focus manually whenever possible.
7. If you can, use a custom button for focusing so that each time you depress the shutter button half-way, the camera won't engage in auto-focusing.
8. Unless you actually need to take multiple exposures with each click, turn that setting off. Most of the time, you just need one exposure per click.
9. Keep the WiFi, Bluetooth, GPS, etc., switched off.
10. Switch off the camera if there's considerable time gap between shots.
11. Keep your camera warm (if the weather is very cold) in between shooting sessions.

There are many ways by which you can extend the camera battery life of a DSLR/ Mirrorless cameras. All these cameras make use of Lithium-ion batteries.

1. Use Viewfinder for shooting.
2. Reduce the number of Image Previews
3. Avoid half-pressing the shutter button for focussing for a long duration.
4. Disable the IS mode when using a tripod.
5. Use Continuous Shooting mode only when it is absolutely necessary.
6. Don't go for third party batteries which comes at a low cost.
7. Use the charger provided along with the camera for charging camera batteries.
8. Use External Battery Grip to get more shots.
9. Switch OFf camera when not in use, sleep mode will also leak some amount of current from the camera battery.
10. Reduce the LCD brightness.
11. Disable the GPS option on the camera, unless you need it.
12. Keep the battery separate from the camera body when not in use (in shelf), the small leakage current can be avoided, which will help to improve the life.

You can find more such tips to extend your camera battery life here in one of my own article, Different Ways to Improve Camera Battery Life