Dijkstra's Algorithm termination

Question

Something must be wrong in my understanding of the algorithm. How is it supposed to work on the following graph.

As I understand it, if the starting vertex is (5) then the algorithm would go, 5->4->1 and then terminate. Vertex (2) would still have infinity as it's weight.

from wikipedia:
if the smallest tentative distance among the nodes in the unvisited set is infinity (when planning a complete traversal), then stop. The algorithm has finished.

Answer 1

No, it would investigate 3 -> 2 after it's done with the 4 -> 1 branch. All children of the currently investigated node are added to the queue, and then from the queue the node with the smallest tentative distance is taken to be processed next.