I've been told my maximum solar system size is 5kW. Is that correct?

The maximum system size you are allowed to connect into the grid is determined by your Distributed Network Service Provider (DNSP). Which may as well stand for: Do Not Serve the People.

You can see who your local DNSP is here.

Most DNSPs say you can only install 5kW of  inverters per phase, unless you want to pay for an expensive and time-consuming 'feasibility study'.

So for all practical purposes the 5kW inverter size limit applies to most single phase households.

But even with a 5kW 'system size limit' you may well be able to install up to 10kW of panels!

How?

By oversizing your solar panel array relative to your inverter as described here.

If you are thinking of microinverters instead of string inverters you can still oversize your system as described here.

The link above describes how you can add 33% more panels than the inverter is rated at without breaking any rules. The system size limit is almost always based on the rated inverter 'AC output'. So you can usually add 6.6kW of panels to a 5kW inverter and still respect the 5kW system size limit. The link above explains why this a good idea.

Further you may even be able to add a bigger inverter and 'export limit' it to 5kW for an even larger panel array. For example you could install an 8kW Fronius inverter and export limit it to 5kW. This would allow up to 8 x 133% = 10.6kW of panels while still respecting the 5kW system size limit. Pretty sneaky eh? This is handy if you have a high winter load and/or batteries. (Thanks to Matthew Wright from Pure Electric for putting me on to this idea.)