Answer
No such numbers exist.
Work Step by Step
Let $x$ and $x+2$ be the odd consecutive integers. Based on the conditions of the problem, then,
\begin{array}{l}\require{cancel}
7x=5(x+2)+54
\\\\
7x=5x+10+54
\\\\
7x-5x=64
\\\\
2x=64
\\\\
x=\dfrac{64}{2}
\\\\
x=32
.\end{array}
Since the solution gives an even number, then no such numbers exist that satisfy the conditions of the problem.
