Here are a couple of Fields medalists' work that had direct practical applications less than 5 years after publication:

Terence Tao's work (with Emmanuel Candès and Justin Romberg) on compressed sensing. Published in 2004-05. By 2007 that was being used for in-vivo MRI reconstruction with substantially undersampled data

June Huh's work on combinatorial Hodge theory was used within 3 years to improve sampling for random spanning forests.

Note that this is only Fields medalists (not all pure mathematics). There have been huge improvements in zero knowledge proofs and homomorphic encryption over the last ~5 years that are also directly applicable to pure mathematics, but no one has a Fields medal for it.