Step 1: Set up algebraic representation

Let the two-digit number be represented as $10x + y$, where $x$ is the tens digit and $y$ is the units digit. The reversed number is $10y + x$.

$10x + y$

Step 2: Apply sum condition

The sum of the number and its reverse is given as 99. Adding them gives $11(x + y) = 99$, which simplifies to $x + y = 11$.

$x + y = 11$

Step 3: Apply difference condition

The difference between the digits is given as 5, so we have $x - y = 5$.

$x - y = 5$

Step 4: Solve the system of linear equations

Adding both equations: $(x + y) + (x - y) = 11 + 5 \implies 2x = 16 \implies x = 8$. Substituting $x = 8$ gives $y = 3$.

$x = 8, \quad y = 3$

Step 5: Form the final number

With $x = 8$ and $y = 3$, the two-digit number is $10(8) + 3 = 83$.

$83$