First let's notice that x2 is nicely featured in both of these functions, and that they're off by a factor of 3 as -0.3 = 3 * -0.1.
Because of this, if we look at the average rates of change on this interval for both f(x) and g(x), you can quickly see by writing down the work that almost everything will cancel conveniently almost immediately.
[-0.1 (5)^2 - (-0.1 (2)^2) ]/(5 - 2)/[-0.3 (5)^2 - (-0.3 (2)^2)]/ (5 - 2) = -0.1 / -0.3 = 1/3
This simplification can be made by factoring out the -0.1 from the top and the -0.3 from the bottom, and what remains will cancel out.
If you're not comfortable with factoring (yet) then simply evaluating the left hand side of the above equality shows that the ratio is indeed 1/3 without simplifying beforehand if you do the calculation carefully on paper (since I'm assuming you can't use a calculator here).
Depending on your teacher you could just say this.
f(x)/g(x) = 1/3 for all x on the interval 2<=x<=5, therefore all average rates of change will obey this ratio. And so long as 0 is not in the interval they're asking you about, this is a fair thing to do. If zero was on the interval, you couldn't do this, as you would technically be dividing by zero here.