[2d]Object following mouse on y-axis, with fixed speed

I’m making a sidescroller game for android/ios, where the object is automatically moving to east. The object would move slowly to mouse y-position. I can’t find out a way for it to do so.

How to make the object follow mouse y-pos with a speed of 5. And as this is for mobile phones, The object should only follow when the screen is pressed.

Use this (How to move a GameObject from his position to a xyz position. - Unity Answers) just alter to move to the Y position only.