The First Minister spoke in Glasgow on Monday as the Scottish Government unveiled a new plan to support use of the technology.
5G is the next generation of mobile network and is expected to offer internet speeds several times faster than the current generation, 4G.
A Deloitte report commissioned by the Scottish Futures Trust suggests 5G could enable Scotland to add about £17 billion to GDP by 2035 and create 160,000 jobs.
Under the plan set out, the Government proposes to fund development of 5G use across the country, as well as continuing to support current projects, along with a range of other measures.
"Our 5G plan sets out the actions we believe are needed to ensure as much of Scotland as possible shares in the vast potential growth on offer," said Ms Sturgeon.
"Our aspiration is to position Scotland as a 5G leader and a forward-looking digital nation.
"5G offers rich potential - opportunities to enhance Scotland's global competitiveness, achieve economic growth and drive innovation across our public and private sectors.
"There are huge potential gains for the public sector if we embrace technologies such as 5G.
"We believe this will be a catalyst for further public sector transformation, enabling high quality, user-focused and efficient services that are driven by data."
Professor Chris Pearce, from the University of Glasgow, said: "5G is a next-generation network technology which is faster, has the potential to revolutionise digital communications and create real social impact in Scotland from public health to the environment.
"Our researchers, led by Professor Muhammad Imran at the University of Glasgow, are developing 5G technologies to facilitate remote health monitoring without invasive measurements and without the need for wearable sensors.
"They are also working to reduce energy consumption and carbon emissions of cellular networks and are developing low-cost pop-up networks.
"These can be deployed quickly and efficiently during large sporting events or disaster scenarios to bring temporary connectivity to the area, strengthening Scotland's resilience capacity.
"The University of Glasgow has been working with academic partners, including the University of Strathclyde and Scottish Futures Trust, on 5G and we are delighted that the Scottish Government's 5G strategy recognises the importance this technology will have in creating services and applications that will benefit our NHS, industry and people right across Scotland."
Andrew McRae, Federation of Small Businesses (FSB) Scotland's policy chairman, said: "Scotland needs to be in the digital fast lane because the next generation of mobile technologies have the potential to boost growth and drive innovation.
"Three-quarters of Scottish businesses say that digital technologies are important to their plans for future growth. But to deliver on this ambition, firms need access to the right skills and high quality digital infrastructure.
"For this reason, decision-makers in Scotland need to do everything they can to ensure Scotland is at the forefront of the 5G revolution. This new 5G strategy is a step in the right direction."