In general, the wave speed in a string depends on the tension in the string and the mass per unit length of the string. When these factors are held constant, the length of the string does not directly affect the wave speed.
The wave speed in a string is given by the equation:
v = √(T/μ),
where v is the wave speed, T is the tension in the string, and μ is the mass per unit length (also known as linear density) of the string. The mass per unit length is determined by the material properties of the string.
In the scenario you described, where the material, tension, and force (amplitude) are the same for both strings, the wave speed would be the same for the 5 m string and the 20 m string. This is because the only factors affecting the wave speed are the tension and the mass per unit length, which are held constant.
However, it's important to note that the wave propagation itself would be different between the two strings. The longer string would have a longer wavelength and lower frequency compared to the shorter string. The wave would take longer to travel from one end of the longer string to the other, but the actual wave speed would remain the same.