What effect would a short circuit have on a solid grounding three phase system, with a grounding resistance 5Ω in comparison to another installation with a grounding resistance of 100Ω?

In a solidly grounded system, you can have the maximum line to ground fault current. As your ground resistance increases, the line to ground fault decreases. Your 1000 ohms ground resistance will give you a smaller line to ground fault than your 50 ohm ground resistance.

Ok. As I understand your question, you are confusing ground fault with the concept of the system connection to earth. They are two totally different things.

As Meynardo points out, with a solidly grounded system, the ground fault current is typically the same or slightly higher than the 3 phase fault current. This current flows from a phase connection to the transformer neural by way of the grounded conductors.

The resistance of that ground system to earth should be kept low because of lightning protection. That is a bit more complicated discussion. For better understanding, read Dave Shipp's IEEE paper on transferred earth potential.

As I understand that your question is about " Earth Fault Current " with different values of grounding resistance.

First, I agreed with Mr. Robert & Meynardo that the Earth Fault Current will be different as the grounding resistance is different, but before any answer, we should know what type of Earthing System is used as we have " TT, TN-S, TN-C, & IT " where :

- If we use " TT " : the commitment of Mr. Robert & Meynardo is 100% right, as the grounding resistance is the most important part when calculating the Fault Impedance Loop.

- If we use " TN-S or TN-C " : there's no any difference, because the Fault Impedance Loop is composed only by the cables' impedances & the source impedance.

- If we use " IT " : depending on realization method, if it's with " one Grounding Point ", and when the 2nd fault happen, the case is exactly the same as " TN-S or TNC ", but if we use " many grounding points but not connected between them ", we will have many possibilities depending on the 1st fault's place and the 2nd fault's place.

The ground resistance should be low to reduce the ground potential rise (gpr) in case of earth fault,This will reduce hazard due to transferred earth potential such as in conductive copper communications lines ,public metal water pipes ,transmission line towers(connected by shield wire to station ground system) .
Although the 1000 ohms ground resistance will give you a smaller line to ground fault than your 50 ohm ground resistance but the GPR =Ig*Rg will be much higher for 1000 ohms(depending on network impedances).

When you have 5 ohms and 1000 ohms it is not considered solidly grounded.

Clarification for Raymond - The 5 ohms and the 1000 ohms are values of the earth ground resistance (due to soil resistivity condition). The system will still be considered solidly grounded if there is no intended resistance or impedance installed between the system grounding point and the earthing grounding electrode, that is solidly grounded system. Now, the earth / soil resistance may be high due to dry condition and nature of the soil that results in higher ground resistance of say 300 ohms, but the system is still solidly grounded because there was no intentional impedance or resistance installed in the line connection going to the grounding electrode.

Grounding resistance will impact:
1) The actual earth fault current (not the prospective fault current). The higher the resistance the lower the earth fault current
2) There will be a change in Earth Potential Rise. The relation is not linear, because EPR=Ig*Rg and as Rg increases, Ig decreases (at different rates - need to consider zero sequence impedance calculation). EPR will impact the touch and step voltage hazards. Refer to IEEE80 for earthing design.
3) If Rg increases and Ig decreases, the protection will be slower to operate. Need to be careful that the protection can reach the fault location ie pickup and trip.
4) Higher Rg can adversely affect any surge protection on the line or substation.
Hope that helps.

The effect of a short circuit in a three phase system is completely independent of which grounding methods has been chosen, or of the resultant ground resistance values.
Only if we have some earth fault, can the earthing (grounding) details cause some differences.