WASHINGTON — Dr. Anthony Fauci on Monday survived a five-year legal deadline to face criminal charges for allegedly lying to Congress about funding risky research in Wuhan, China — but he isn’t out of the woods, The Post has learned. Fauci testified to a Senate committee on May 11, 2021, that he did not fund “gain of function” research that genetically altered coronaviruses in the same city where the COVID-19 pandemic started — as he tried to tamp down the now-dominant “lab leak” theory. Evidence shows he did. The country’s former top infectious disease official still could face other potential charges for lesser-known contested testimony, or for alleged conduct stretching closer to the present day, such as for conspiracy, insiders said, even though his best-known alleged crime went uncharged. Dr. Anthony Fauci isn’t out of the woods — despite surviving a five-year deadline to face charges for allegedly lying to Congress.…