The reciprocal of \(5\) is \(\frac{1}{5}\).
The reciprocal of a number, let's say \(x\), is \(\frac{1}{x}\).
(I'm assuming both are reciprocals because you said reciprocals.)
\(\frac{1}{5} + \frac{1}{x} = \frac{8}{11}\).
We need to put this under a common denominator, our smallest one being \(55\).
\(\frac{11}{55} + \frac{1}{x} = \frac{40}{55}\).
\(\frac{1}{x} = \frac{29}{55}\).
Cross multiplying, we get
\(29x = 55\).
\(x = 55 \div 29\).
\(x = 1.89655...\)
You can round this to any digit needed, but I'm going to round it to the hundredths, making our answer \(\boxed{1.90}\).
