The current one$-$year interest rate is $5\mathrm{.}5\%,$ and the expectations for the one$-$year interest rates over the next four years are as follows: $5\mathrm{.}3\%,5\mathrm{.}1\%,4\mathrm{.}9\%,4\mathrm{.}7\%$

Using this information, $(1)$ calculate the interest rates of bonds with maturities of two to five years using the Pure Expectation Theory. $(2)$ Describe the type of yield curve that results.