Andy Murray entered the top 4 on September 8th, 2008 - which is the first week of the Big Four holding the top four spots. Here are the most weeks in the top 5 by players who played alongside the prime of the Big Four, from 2008 to the present. Some of the weeks might be before that time (e.g. Davydenko, Roddick, Hewitt), but I thought I'd include their totals.
bold: Big Four
Normal: Players who were top 5 Sept 8, 2008 or later
787 Federer
681 Nadal
573 Djokovic
429 Murray
208 Roddick
190 Ferrer
184 Hewitt
171 Wawrinka
149 Davydenko
111 Del Potro
88 A Zverev
74 Nishikori
59 Soderling
33 Cilic
32 Dimitrov
29 Berdych
25 Raonic
21 Thiem
12 Tsonga
11 Anderson
3 Robredo
Players like Hewitt, Safin, Ferrero, Coria, and Nalbandian were all top 5 before the rise of the entire Big Four, in the Fedal era.
The bulk of Roddick's, Hewitt's, and Davydenko's weeks in the top 5 were before Sept 8, 2008, but all had weeks in the top 5 after. Ferrer spent some time in the top 5 before that date, in late 2007 and 2008, but most of his weeks were in the Big 4 era...but less than Wawrinka, I think, who was probably the non-Big Four player with the most weeks in the top 5 during those years.