The following is from first hand experience. I currently have the guts of an iPhone SE in a custom blue 5s housing with silver buttons and sim tray.

You won’t get away with swapping just the motherboard alone. At the very least, I believe the battery, camera, the volume/power/flash flex cable and the headphone/microphone/lightning flex cable are different, so those will have to follow the motherboard. The top antenna appears to be identical, but don’t be surprised if you need to swap it too.

Housings are identical except for one small detail in the corner around the rear camera. The power/volume/flash flex has an extra branch on the SE that wraps around the camera. The SE housing has a recess cut in the corner to accommodate this. Also, the SE has a rubber pad between the camera and housing which has a bit of a tab that extends into the recess, covering this flex from the camera.

You can put the SE top flex into a 5s housing, but there will be a bit of excess length for the available space. You can work this extra loop around to just behind the power button and away from the Camera, and either install the rubber pad a little out of place or just omit it altogether. Kinking this extra wrinkle may damage it, but I don’t know what functionality this would affect (might be NFC).

Alternately, if you have the means to cut the appropriate recess into your 5s housing, then everything can go together as intended. Screw locations are absolutely identical and the motherboard fits in the housing, no problem.