Is it possible to power a monitor with 5 V if the power supply specification is DC 9-36 V?
You could go two ways:

Use a higher input voltage and step it down like you had mentioned
Use the lower 5V voltage and use a boost converter to power the monitor alone

However, after reading some of your comments about powering this thing with a 5V battery and you being new to electronics I have to warn you about the following. Even if you use a 5V battery you will need a voltage regulator after it because batteries never offer constant voltage. Instead they start at a high voltage (i.e. 5.5V) when fully charged and can decrease their voltage when they lose charge. There's no way escaping a regulator after a battery.
Therefore, I would recommend going with a higher voltage battery (i.e. 9V or 12V) and use a step down converter for your digital and a boost converter for your monitor.