Sorry i am such a disappointment to you. But it does not take the vast research me and many others do to get a good basic knowledge of tennis history. Less than a half-dozen books you need. As to achievements in the Pro game, The Professional Tennis Archive by Chris Jordan is available on Amazon and has the most reliable and thorough records. There is no reason not to know.
Right at his 37th birthday, Segura won the 1958 Masters. This would be like going undefeated at the ATP Finals, which counts extraordinary to me because he went 6-0, defeating Gonzalez, Rosewall, Hoad, Sedgman, and Trabert, along w Hartwig (a good player). The Master RR would be like the ATP Finals in prestige. Earlier, a few months shy of 36, he won the 1957 Sydney T.O.C., a tournament so close to a Major that there are posters here (and certain eminent former posters) who count all six of the T.O.C.s as Majors. Oh, and Segura at 37 played 27-year old Trabert to an effective draw in their 69-match tour. Later that season, playing against peak Hoad, the emerging Rosewall, Trabert and occasionally Gonzalez in the 1958 European Tour, Pancho went 22-27 - "holding his own." And beyond. The following year he came within a couple of points of winning Wembley. The next, now 39, he beat Hoad and Sedge (and Nielsen, the two-time Wimbledon finalist) September 1960 at Wembley, then lost in four sets to Rosewall. In the summer of 1961, he won three straight pro tournaments. Between age 36 and 41, Segura made the finals at five traditional Pro Majors (at least once at each). In the category of greatest players after 35:
Rosewall
Tilden
Each of the Big Three
Gonzalez
Connors
Segura
Kozeluh
Drobny
Maybe?