I have lets say 5 individual vertexes objects with the origin all set to the centre of the screen. How could I set each vertex to the geometry of each vertex?
In 2.79, in object mode, with all objects selected, ShiftCtrlAltC will send the origins of all the objects to their geometry simultaneously.
in 2.8, until you set a personal shortcut, it's available only through the header > Object > Set Origin menu.
Or, Enable the shipped add-on '3D Viewport Pie Menus' > 'Origin Pie'.. which has the advantage of working in Edit Mode. That lets you set the origin to a selection of the geometry.