I am unable to upload the image of my trials.
I assumed the radius of small circle is $x,$ horizontal distance between the centers of two circles is $y.$
I have joined the centers of the two circles and the length is $(5+x).$
I have drawn a vertical line from the center of the bigger circle to the center of the semi circle.
I have also drawn a horizontal line from the center of the small circle to the above line.
Then, by applying Pythagoras theorem, I get
$$(x+5)^2=(5-x)^2 + y^2.$$ I need one more equation to solve for $x.$
Intuitively I wonder if the radius of the small circle could be half of the big circle. I carefully constructed it and got $2.5 cm$ as the radius but I am not sure.