The site you linked to is vBulletin 4.x. It would be very difficult, if possible at all. to duplicate that style for VB 5.x. However it is basically the default VB 4.x style with a custom logo so you could easily duplicate the look by running VB 4.x. The most recent (but likely last) version of VB 4.x was just released, VB 4.2.5 and will work with PHP as high as 7.1.x (and as low as 5.6.x.)
vBulletin 5.x ships with a number of build in styles, you can see examples at
www.vbulletin.com/forum/ and using the style selector at the bottom left of most pages.