Canon PIXMA mg5420 error #1405 - PIXMA Canon Office Equipment & Supplies

Hold the "STOP" button down for 10 seconds and see if that clears it.

Canon PIXMA MG5420 Setup Guide

This is the 23 page guide, there is also a 4 pg quick start guide on
that site.
Canon PIXMA MG5420 Manual

Try removing cartridge, turning printer off/on and installing the cartridge back in. Try this couple of times and if it doesn't work, replace the cartridge.1403 indicates 'not recognised' cartridge and there is no way to reset this condition.

Canon Support Drivers PIXMA MG5420

Here you can find the driver according to your Operating System.

This is consistent with any of error codes 1401, 1403 and 1405. It indicates a problem with the print head.
Per Canon the resolution of these errors 'requires the assistance of a Canon authorised service facility. Please use the link at the top of the page to locate your nearest facility.'
From Canon error page for 'Orange light blinking 5 times':

1401/E05
Description: The print head is not installed or has not been properly installed.

1403
Description: A print head temperature sensor error has occurred.

1405
Description: Faulty data of the print head.

http://www.canon.co.uk/support/consumer_products/product_ranges/printers/pixma/error_codes/

Cannon pixma 3500 Flashing orange light count the blinks for the error,

You may have accidentally installed updated firmware in your printer, so it doesn't recognize the carts anymore. You may have to "reset" the chips on your carts.
If resetting the carts doesn't help, I'd suggest contacting the place you got the refillable carts.

Try opening control panel>devices&printers. Set the paper feed to the upper feed as permanent. Then on printer itself make sure that paper type, size and feed is where you want it.

If all else fails try this:
(at your own risk)
1. Turn on the printer
2. Open the rear cover and remove the paper feeder there
3. Insert a sheet of paper from the rear (in the slot at where the paper feeder just was.
4. turn off the printer
The printers rolls will spin as it shuts down and it will pull in the paper, hopefully clearing the paper sensor.

This worked for my MG5420