Problem

If you lend someone a dollar and get it back $5$ years later with a total of $2.0113571875$ dollars in principal and interest, what is the annual interest rate?

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If the annual interest rate is $r$, the total principal and interest at the end of the fifth year is
$$1×(1+r)^5=1+5r+10r^2+10r^3+5r^4+r^5=2.0113571875,$$
$$∴ \quad r^5+5r^4+10r^3+10r^2+5r-1.0113571875=0.$$
Solving this quintic equation,
$$(r-0.15)(r^4+5.15r^3+10.7724r^2+11.615875r+6.74238125)=0. \qquad [*]$$
Since all four solutions of $r^4+5.15r^3+10.7724r^2+11.615875r+6.74238125=0$ are complex numbers, they are inappropriate.

Therefore,
$$r-0.15=0,$$
$$∴ \quad r=0.15.$$

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[*] The following high-precision calculation site was used:
https://keisan.casio.jp/exec/system/1436509596  

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Reference

Yoshikazu Yamakawa, ed. (1997) Okayama ken no Sangaku (Sangaku in Okayama Prefecture), pp.27-28; pp.398-399.