Given f(x) = -log3 x, find the domain of f, the equation of f⁻¹, and the transformation from f⁻¹ to h(x) = 3^x - 5.

For a logarithmic function $\log x$ to be defined, its argument $x$ must be strictly positive. The negative sign in front of $\log x$ does not affect the domain.
The domain of $f$ is $\boxed{\text{}x > 0\text{}}$

Given the context of part 5.3, where $h(x) = 3^x - 5$, it is implied that the base of the logarithm is 3. So, $f(x) = -\log_3 x$.
Let $y = -\log_3 x$.

Multiply both sides by $-1$:

Convert the logarithmic equation to an exponential equation:

The equation of $f^{-1}(x)$ is $\boxed{\text{}y = 3^{-x}\text{}}$

From 5.2, $f^{-1}(x) = 3^{-x}$.

We need to transform $y = 3^{-x}$ into $y = 3^x - 5$.
First, to change $3^{-x}$ to $3^x$, we reflect the graph of $y = 3^{-x}$ about the y-axis (replace $x$ with $-x$). This gives $y = 3^{-(-x)} = 3^x$.
Next, to change $3^x$ to $3^x - 5$, we translate the graph of $y = 3^x$ vertically downwards by 5 units.
The transformation is a reflection about the y-axis followed by a vertical translation of 5 units downwards.

Given $f(x) = -\log_3 x$.
A reflection about the x-axis