Catalysis of the reaction: [eIF5A-precursor]-lysine + spermidine = [eIF5A-precursor]-deoxyhypusine + propane-1,3-diamine. Four sub-reactions have been identified,in which the intermediates remain tightly associated with the enzyme: spermidine + NAD+ = dehydrospermidine + NADH; dehydrospermidine + [enzyme]-lysine = N-(4-aminobutylidene)-[enzyme]-lysine + propane-1,3-diamine; N-(4-aminobutylidene)-[enzyme]-lysine + [eIF5A-precursor]-lysine = N-(4-aminobutylidene)-[eIF5A-precursor]-lysine + [enzyme]-lysine; N-(4-aminobutylidene)-[eIF5A-precursor]-lysine + NADH + H+ = [eIF5A-precursor]-deoxyhypusine + NAD+.