The relation you have shown is not a function.
In order to be a function, a relation's domain must be continuous in that no x-value is not repeated in any of the points. Since the first two points of the relation are (5,1) and (5,3), you can see that they have the same x-value, meaning that this is not a function.
One quick way you could test this is to quickly sketch a graph and use the vertical line test to see if the relation in question is a function. If it cross the vertical line once in all places, it is a function - if it crosses the vertical line more than once in any place, it is not a function.
