Diagnosis
Yes, you can turn them off. The RT-AX55 has a built-in LED on/off control, but it's buried in the administrative settings, not on a physical button.
How to Fix It
You need to log into the router's web interface. 1) Go to Administration. 2) Click the 'System' tab. 3) Look for a setting labeled 'LED illumination' or simply 'Turn LED ON/OFF'. 4) Set it to 'OFF'. 5) Click 'Apply'. The lights should go dark immediately. They'll stay off even after a reboot.
If That Didn't Work
If you can't find that option, your firmware might be old. Check for a firmware update first (Administration > Firmware Upgrade). Newer ASUS firmware versions definitely have this toggle. After updating, the setting should appear.
Heads Up
With the LEDs off, you lose the visual status cues (like the red internet light). If you have connection problems later, you might want to temporarily turn them back on to see if the router is indicating an issue with its lights.