Niko is 27 inches shorter than his father, who is 5 feet 10 inches tall. How tall is Niko?
(1 foot $=12$ inches)

If Niko's father is 5 feet 10 inches tall, he is 5 feet $\times (12$ inches/ 1 foot $)+10$ inches $=70$ inches tall.
If Niko is 27 inches shorter, he is $70-27$ $=43$ inches tall,
which is equivalent to 43 inches $\times (1$ foot $/12$ inches $)=3$ $7/12$ feet, or 3 feet 7 inches,
so the correct answer is $\mathrm{C}$.