y= 16/(x+2)²

dy/dx = -2(16)/(x+2)³

            = -32/(x+2)³

dy/dx = dy/dt* dt/dx = 0.25/-0.05 = -5

-5 = 32/(x+2)³

x= (32/5)^1/3 -2 = 2(4/5)^1/3 -2

When x= 2(4/5)^1/3 -2,

y = 4(4/5)^-2/3

Note: your written working dy/dx on the question is wrong as the order of differentiation in the numerator is reverse. Also note the minus sign for dx/dt for decreasing x. 

Pls refer to https://www.mathcentre.ac.uk/resources/uploaded/mc-ty-quotient-2009-1.pdf

there must be a minus sign for this question for the dy/dx, you have reverse the order in the numerator resulting in no minus sign.