Introduction:
In this scenario, we are given the resistance values of a platinum wire thermometer at the ice point and steam point, as well as the resistance measured when the thermometer is inserted into an unknown hot bath. Our goal is to determine the temperature of the hot bath using this information.

Given Information:
- Resistance at ice point = 5 Ohm
- Resistance at steam point = 5.25 Ohm
- Resistance in the unknown hot bath = 5.5 Ohm

Understanding the relationship between resistance and temperature:
The resistance of a wire is directly proportional to its temperature. This relationship can be expressed using the formula:

R = R0 * (1 + α * ΔT)

where:
- R is the resistance at a given temperature
- R0 is the resistance at a reference temperature
- α is the temperature coefficient of resistance
- ΔT is the change in temperature from the reference temperature

Determining the temperature coefficient of resistance:
To determine the temperature coefficient of resistance (α), we can use the resistance values at the ice point and steam point. Rearranging the formula, we get:

α = (R - R0) / (R0 * ΔT)

Substituting the given values, we have:

α = (5.25 - 5) / (5 * 100)

Here, we assume that the temperature difference between the ice point and steam point is 100 degrees Celsius.

Simplifying the equation, we find that α = 0.005.

Calculating the temperature of the hot bath:
Now that we know the temperature coefficient of resistance, we can use the formula to calculate the temperature of the hot bath.

R = R0 * (1 + α * ΔT)

We can rearrange this formula to solve for ΔT:

ΔT = (R - R0) / (R0 * α)

Substituting the given values, we have:

ΔT = (5.5 - 5) / (5 * 0.005)

Simplifying the equation, we find that ΔT = 20 degrees Celsius.

Conclusion:
Therefore, the temperature of the hot bath is 20 degrees Celsius.