Unity 2D Scripted Movement

In simple code without external libraries (sometimes I prefer my own code for simple things, easier to understand and debug than someone else's)

 public class ObjectMover {
     private Vector3 target;
     private Vector3 start;
     private float totalTime = 0; // when set to 0, will not move
     private float currentPosition = 0;
 
     public void Update() {
         if (totalTime > 0) {
             currentPosition += Time.deltaTime / totalTime; // advance position by the fraction of the total time that passed this last frame
             if (currentPosition >= 1) {
                 currentPosition = 1; // don't pass the target
                 totalTime = 0; // end the movement when reaching the target
             }
             transform.position = Vector3.Slerp(start, target, currentPosition); // position the object between the start and the target relative to the time passed out of the total time
         }
     }
 
     public void MoveTowards(Vector3 direction, float distance, float time) {
         target = transform.position + direction.normalized * distance; // set destination location
         totalTime = time; // set time to perform the movement
         if (time == 0) {
             transform.position = target;
         }
     }
 
     public void CancelMove() {
         totalTime = 0;
     }
 }

Not to use it, you would attach the ObjectMover script to any object you wish to be movable this way, and then call it this way to move it up 3 units in 5 seconds, as in your example:

 GameObject objectToMove = GameObject.Find("SomeObjectName");
 objectToMove.GetComponent<ObjectMover>().MoveTowards(Vector3.up, 3, 5);

Of course you can use object references instead of GameObject.Find.