It says a lot about tech companies that many consider "small" constitutes those with market caps below $10bn. As the world recalibrates after the disconnection instigated by the covid pandemic, smaller software companies have been dealt a unique opportunity to take advantage of new communication and working models. One only has to look at the rise of ZOOM as recognition of this. Such companies typically operate as "software as a service" (SaaS) organizations, producing data-driven tech such as cloud services and cybersecurity. Others are more hands on, providing sleek interfaces for communication and creative software. The sector is vast, which is why it's not surprising there are plenty of public companies in this $5bn-10bn ballpark.
This Spark lists some of the lesser-known but just as impressive software companies in the US, all with market capitalizations that range from $5bn-10bn. Make sure to DYOR before making a trade, though. This is not investment advice.