This question is an example of the role played by forces internal to a system. In the case of the human body, complex chains of metabolic processes provide the energy used to contract muscles. Furthermore, different metabolic pathways with different efficiencies will be deployed depending on the human's speed, current dietary situation (does their body have access to carbohydrates? Is the body burning more fat or ketones?), and many more variables. This heavily complicates the question.
Fortunately, to answer your question, we don't have to worry about that. All we have to do is treat the human like a black box and measure its energetic expenditure in different situations. For the sake of getting a clear answer, let us assume that we are dealing with an average human who just had a nice big plate of pasta the night before. In this average case, we can say that a human has $S=.55m^2$, $C=1.16$, and that air has $\rho=1.225 kg\cdot m^{-3}$. ( These values are from a very well sourced school project)
Now, let's compare two situations: 1) as in your posed question, we can consider only the force of air resistance at various speeds to calculate energy expenditure, and then 2) use measured values from the literature for the power required for an average human to maintain certain speeds to calculate the energy expenditure.
1) First, let's consider a modest jog of 2.25 m/s. Using the quadratic drag force equation $F=\frac{1}{2}C\rho S V^2$, this yields a constant drag force of 1.98 if we assume there's no wind. The work done is $$W=\int_0^d{F\cdot dx}=\int_0^d{1.98dx}=1.98d$$
where d is the distance traveled. For a 5K run, this yields
$$W=1.98\cdot 5000=9900J\approx 2.4\ kcal$$
since $1\ J\approx .00024\ kcal$.
If the runner was going at a 6 min/mile pace (~4.5 m/s), a similar calculation gives $F=7.81$ and $W\approx 39000\ J\approx 9.4\ kcal$. But notice that the kinetic energy of a runner of 70 kg moving at this rate is $T=\frac{1}{2}\cdot 70\cdot 4.5^2\approx 700\ J $. This is about 7% of the energy used to run the 5K itself!
2) Following this Harvard Medical School Table we can do some very rough obsevations that show the difference between running at different speeds. At 2.25 m/s, we see that a a 5K would take about 35 minutes to complete, so the energy expenditure would be somewhere around 350 kcal. At 4.5 m/s, a 5K would take about 18.5 minutes and expend about 380 calories. Now, the difference here may be small, but it of course scales as longer distances are ran.
Finally, we have to take into account the basal metabolic rate- the Harvard table does not separate this from its values. If we assume that the runner is a 5'8" man who is less than middle age and is 70 kg, he will have a BMR somewhere around 1700 kcal/day. This means that his body will spend about 40 kcal while jogging for ~35 minutes at 2.25 m/s, and about 20 kcal while running the 5K at 4.5 m/s. If we take this into account, the difference becomes $360\ kcal- 310\ kcal = 50\ kcal$.
In conclusion, we shouldn't rely upon knowledge of drag force to determine how much energy is being spent, and the mechanisms used by the human body to move our muscles become less efficient as we move faster.
