Adding the following code will fix your problem (code is in Swift):
scene.scaleMode = SKSceneScaleMode.ResizeFill
Now if you want to know why this fixes your problem, what your problem actually is, and how to handle multiple resolutions – I suggest you continue reading.
There are three things that can impact the position of nodes in your scene.
1) Anchor Point
Make sure your scene's anchor point is set to (0,0) bottom left. By default the scene's anchor point starts at (0,0) so i'm assuming that is not causing the issue.
2) Size
Check the size of your scene. I typically make my scene size match the size of the device (i.e. iPad, iPhone 4-inch, iPhone 3.5 inch), then I place another layer in the scene for storing my nodes. This makes me able to do a scrolling effect for devices with smaller resolutions, but it depends on your game of-course. My guess is that your scene size might be set to 320, 480 which could be causing the positioning problems on your iPhone 5s.
3) Scale Mode
The scale mode has a huge effect on the positioning of nodes in your scene. Make sure you set the scale mode to something that makes sense for your game. The scale mode kicks in when your scene size does not match the size of the view. So the purpose of the scale mode is to let Sprite Kit know how to deal with this situation. My guess is that you have the scene size set to 320,480 and the scene is being scaled to match the iPhone 5 view which will cause positioning problems identical to what you described. Below are the various scale modes you can set for your scene.
SKSceneScaleMode.AspectFill
The scaling factor of each dimension is calculated and the larger of
the two is chosen. Each axis of the scene is scaled by the same
scaling factor. This guarantees that the entire area of the view is
filled, but may cause parts of the scene to be cropped.
SKSceneScaleMode.AspectFit
The scaling factor of each dimension is calculated and the smaller of
the two is chosen. Each axis of the scene is scaled by the same
scaling factor. This guarantees that the entire scene is visible, but
may require letterboxing in the view.
SKSceneScaleMode.Fill
Each axis of the scene is scaled independently so that each axis in
the scene exactly maps to the length of that axis in the view.
SKSceneScaleMode.ResizeFill
The scene is not scaled to match the view. Instead, the scene is
automatically resized so that its dimensions always matches those of
the view.
Conclusion
It looks like you want to remove the scaling of your scene, that way your positions in the scene will match the actual positions in the view. You can either set your scene's size to match the view size, in which case no scaling will take place. Or you can set your scene's scale mode to ResizeFill which will always make the scene's size match your view's size and it won't scale anything. In general I would stay away from any scaling and instead adjust the interface and the scene size to best suit each device. You may also want to add zoom and/or scrolling to allow devices with smaller resolutions to achieve the same view field.
But what if I want to scale my scene?
If however you need to scale your scene, but you still want positions to be relative to the view (i.e. You want (0,0) to be the bottom left of screen even when scene is cutoff) then see my answer here
Additional Info
See answer here for sample code showing how I layout nodes dynamically.
See answer here for more details about scaling to support multiple devices.
