Just burned my first LCD... but why?
The tutorial you followed says

On the vast majority of LCDs (including ones from Adafruit) the LCD includes a series resistor for the LED backlight.
If you happen to have one that does not include a resistor, you'll need to add one between 5V and pin 15. To calculate the value of the series resistor, look up the maximum backlight current and the typical backlight voltage drop from the data sheet. Subtract the voltage drop from 5 volts, then divide by the maximum current, then round up to the next standard resistor value.

The datasheet says

LED BACKLIGHT CHARACTERISTICS

COLOR         Wavelength Operating         Spectral line half   Forward Current 
              λp(nm)     Voltage(±0.15V)   width Δλ(nm)         (mA) 
Yellow-green  --         4.1               --                   100


NOTE: Do not connect +5V directly to the backlight terminals. This will ruin the backlight.