You can accurately calculate the Voltage drop in each diode from theoretical Shockley equation if you know all the parameters of which diodes are used.
This is not how I would compute the answer in an exam, but rather as a design engineer, choose a diode and see the exact results.
The better way is to choose a common diode and read the datasheet curves to compute the effective voltage drop at the estimated current where that slope represents the incremental or effective series resistance (ESR) with a small offset voltage which we know is 26mV @20'C at zero current for a silicon diode. But we can neglect this for practical reasons.
The most common old small signal silicon diode was the 1N4148. We know one diode will be in reverse league mode and hence have most if not all the voltage drop, and will be much higher impedance than your 10 MOhm DMM so you would not be able to measure its impedance or voltage drop using this method, but we can calculate its voltage drop directly from Figure 2 & 3. You may be inclined to extrapolate the curves since the applied voltage is only 5V and diode leakage drops with voltage like a linear resistor. You may find fixed leakage currents at a fixed voltage, but better datasheets such as this show the actual behaviour over a wide range of currents. But again for practical reasons when you get down to nanocurrents, you can round off.
So why not measure the typical Resistance of reverse leakage @20'C as shown for typical diode datasheet.
Then do the same for the other diode using this effective current limit in micro or nanoamps to determine the forward voltage. This too you may find "off the chart edge" so we can round off the values to say, "3 significant figures" and know exactly what these values are.
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So again we know the current is same thru both, but one is forward biased while the other is reverse biased so let's call it Vf and Vr, where Vf+Vr=5V in this question.
Although it is an academic question ,
What is Vf ?
What is Vr ?
- such that total adds up to 5V for this example.
ref : datasheet and distributor pricing