let's take some assumptions :
Vs1 = V + dV
Vs2 = V - dV
Diode : diode + internal resistor = Rb (real diode)
current circulating in the first diode = i1 current
current circulating in the 2nd diode = i2 total
total current in resistance = i
i1 + i2 = i
i1 = (Vs1 - Vd - Vr)/Rb i2 = (Vs2 - Vd - Vr)/Rb i = Vr/R
(Vs1 - Vd - Vr)/Rb + (Vs2 - Vd - Vr)/Rb = Vr/R .
(V+dV - Vd + V-dV - Vd)/Rb = Vr(2/Rd + 1/R)
with Rb = 1 ohm .
2V - 2Vd = Vr(2R + Rb)/R
Rb <<< R
Vr = V - Vd = 5-0.7 = 4.3 V
Vd1 = 5.001 - 4.3 = 0.701 V (+ 1 mV across Rb1)
Vd2 = 4.999 - 4.3 = 0.699 V (- 1 mV across Rb2)