As the temperature of soil decreases from 10°C to -5°C, what will most likely happen to the infiltration rate of water through it?

A drop from 10 to -5 degrees C will most likely slow the infiltration rate. Infiltration rate is the rate at which ground water is absorbed into the soil, either from rainfall or irrigation. It is affected by other factors as well, such as gravity, capillary action, and porosity of the soil. But with a temperature drop such as the one you ask about, freezing of the water is going to take place, as the freezing point of water is 0 degrees C. If the ground is already filled with water when this temperature drop takes place, a layer of frozen ground and water forms, and little to no more water can be absorbed. It has to be a long, sustained freeze for this to be true for a very large area, though; otherwise, there will still be some parts that are not solid, and can still absorb some water.