My GTAV online loading times triple whilst running teamspeak 3, Sometimes will fail over and over again sometimes connect and play, With teamspeak off no issues fast loading times even if i change sessions consecutively, i also use a xbox 360 controller and had to disable the hot key addon otherwise my controller stop responding.
Do you have plugins/addons enabled on ts3 that connect to gta5 or something?
Do you have GTA5 on fullscreen? If not, then do that. If GTA5 is not running 100% in the foreground, the loading times are very high.