Can I use BC558 PNP transistor with 5V DC supply?
You should use this circuit 







simulate this circuit &ndash; Schematic created using CircuitLab

And need to work in saturation region so please read this
Bjt base current calculation

And in your case \$ V_{CC} = 5V \$ and \$I_{led} = 5mA\$ we have 

$$R_C \approx\frac{V_{CC} - V_{led}}{I_{led}} \approx 470\Omega...680\Omega$$

Depend on the LED color. 

$$R_B = \frac{V_{IN} - V_{BE}}{ \frac{I_{led}}{10}} \approx \frac{4.3V}{0.5mA} = 8.6k\Omega $$ 

In practice, I will use \$10k\Omega\$ 

And for PNP I need more info. Because we need to know from where the signal at the base is coming from, and his voltage range.  

But in general, the circuit diagram will look something like this 







simulate this circuit