It's a 5.1 ohm resistor.
Your multimeter may not beep or say "continuity" if the resistance is higher than some value ... let's say 1 ohm.
There is some tolerance because the leads of your multimeter have some resistance (typically under 0.25 ohm) and the tips of your probes could also be dirty enough to introduce some resistance. So in continuity mode, a meter would beep and show continuity when the resistance is below some threshold.
5.1 ohm may be just big enough to not register as a short in your multimeter and won't trigger the continuity.
In diode mode, your meter outputs a specific voltage from one probe to the other and it measures the voltage drop on the other probe. There is a voltage drop across the 5.1 OHM resistor, so your meter may detect the resistor as a diode... but it will show some voltage drop regardless of how you position the probes.
Put your multimeter in the resistance mode and touch probes together and the meter, if it's good enough, it should show around 0.1 ohm.. 0.25 ohm ... my own probes are 0.2 ohm (uni-t ut61e)
Here, I made you a video with my phone ... may have to look at it sideways, too lazy to do it again or edit it :
https://drive.google.com/file/d/13uWUNq53IWjEbKiaqxT54Pyy9pO4Pw0s/view?usp=sharingresistance of probes
resistor is 1 kohm , showing you meter reads it at 996 ohm (good enough)
then you see the meter in diode mode,
and reading again resistor it shows 1.06v drop across the resistor, so the meter thinks it's a diode
reverse probes and measure again, same value
then see diode and the big pads...
measuring voltage drop across diode shows 0.18v (typical for a schottky diode)
the probes reversed you see OL or 1.7v (that 1.7v is consequence of how circuit is, there's a capacitor or inductor in parallel with the diode messing the measurement)
then going back to meter in continuity mode, to show the meter won't show continuity across resistor because 1 kohm is too much.