[Plugin: Visual Composer] Causing Severe Page Load

I have come here because I am not sure where else to go. I have been having a problem where a site I created for a school district high school is taking an UNBELIEVABLY LONG time to load the last time I tried to visit the site the homepage took 5+ minutes to load. I have never seen anything like this. I determined that when I deactivate the “Visual Composer” plugin the site runs fine. As soon as I activate it again, the load time is unbearable. I’ve contacted WPBakery and was told that it’s the theme that I am using. I’ve contacted the theme developer and was told what to do based on WPBakery’s suggestions and still the issue hasn’t been resolved. In fact it seems to have gotten worse over time. I am not sure what to do at this point, and was hoping someone could point me in the right direction. Looking at the network analysis in Chrome it appears that upon requesting a page the server just sits there forever waiting and then something happens and everything loads in a split second. I have loaded a brand new wordpress installation, and while the issue seems to be somewhat resolved the load time is still sketchy. Can someone please give me some clue as to what could potentially cause the page to basically hang when it is requested. WPBakery also mentioned that we need to be running a newer version of PHP. We are currently running 5.4.40 and was told we need to be running. 5.6 would the PHP version cause this severe of an issue?