This perspective paper delves into the concept of foundation intelligence that shapes the future of smart infrastructure services as the transportation sector transitions into the era of Transportation 5.0. First, the discussion focuses on a suite of emerging technologies essential for foundation intelligence. These technologies encompass digital twinning, parallel intelligence, large vision-language models, traffic simulation and transportation systems modeling, vehicle-to-everything (V2X) connectivity, and decentralized/distributed systems. Next, the paper introduces the present landscape of Transportation 5.0 applications as illuminated by the foundational intelligence, and casts a vision towards the future including cooperative driving automation, smart intersection/infrastructure, parallel traffic management, virtual drivers, and mobility systems planning and operations, laying out prospects that are poised to redefine the mobility ecosystem. Last, through a comprehensive outlook, this paper aspires to offer a guiding framework for the intelligent evolution in data generation and model calibration, digital twinning and simulation, scenario development and experimentation, feedback loop for management and control, and continuous learning and adaptation, fostering safety, efficiency, reliability, and sustainability in the future smart transportation infrastructure.