GB,
ADB generally recommends 60 per floor for a single staircase - but not for a spiral 750mm staircase with open doors over 5 storeys. ADB is not designed to deal with such buildings. It says,
"...adherence to the guidance in this document might prove unduly restrictive. In such cases it would be appropriate to take into account a range of fire safety features, some of which are dealt with in this document and some of which are not addressed in any detail and to set these against an assessment of the hazard and risk peculiar to the particular case."
This supports the replies so far.
As kurnal and ADB allude to, some leeway might be in order in such cases. But only if justifiable. Five storeys is a long dead end and a spiral staircase is a difficult route. 150 sounds like a lot of people to put in such a situation.
Possible solutions might be along the lines of L3 detection (or better) and fire doors on magnets to the stairs or ever present staff trained to shut doors on the alarm. Alternatively, these buildings often have a pretty low fire loading and it might be acceptable to do without fire doors if it can be all but guaranteed that there will never be a fire that affects the escape route. That might be a tall order.
150 people makes it sound like an unusually popular hertitage building. Often, these buildings have a very low population (e.g. 8 ) for 99% of the time and only have large numbers (such as 150 or 200, as proposed here) when they have special functions or exhibitions. If this is the case here, then you can consider having two fire safety strategies - one for when the building has a population of 8 and one for when the popular functions are on and a heavy staff presence is required. That doesn't mean that you can chuck out the fire safety rules when just 8 are there - I might be one of those 8!
Stu