If y is a function of x, and x is a function of t, then, by composition of functions, y is also a function of t. To find the derivative of y with respect to t, we use the chain rule in the form
Eq.1) dy/dt = (dy/dx)⋅(dx/dt)
Note that in this equation, if we wish to find dy/dt at a particular value of t (say to), we must evaluate dx/dt at to, and evaluate dy/dx at the value of x corresonding to to (call it xo). From the information given in the statement of your problem, we wish to find dy/dt at a value of t (not specified) when x = 2 and dx/dt = 5. Given
y = x3 + 2x,
dy/dx = 3x2 + 2.
We evaluate this when x = 2 to obtain
dy/dx = 3(2)2 + 2
dy/dx = 14
Now substituting the required information into the chain rule (Eq. 1), we have
dy/dt = 14⋅5
dy/dt = 70.
Hope that helps! Let me know if you need any clarification.