One really should define what is meant by "activity" before proceeding. Is it kcat or kcat/Km? They often give different pH profiles, and the pKa values of enzymatic groups often change when substrate binds. It would also be helpful to whether the rate being measured is for one full catalytic turnover, or for the hydrolysis of the intermediate, the 2', 3' cyclic phosphodiester (this is the second half reaction). My understanding is that one sees similar results for the substrate versus the intermediate (Hammes, 1969), but I am not certain.
However just taking the pH-rate profile that is given and assuming that we are talking about the second half-reaction, I would reason as follows: The pKa of 5.4 represents a group which must be deprotonated for the reaction to proceed (activity decreases as pH is lowered beyond that point). This might be a base or a nucleophile (if we were studying a different enzyme), but for ribonuclease it is probably a base. In the drawing of the second half-reaction, the base is His119. The pKa of 6.4 represents a group that must be protonated for the reaction to proceed (activity decreases as pH become greater than this). This might be a general acid. For the second half-reaction of ribonuclease, the general acid is His12.