Five thousand. Any higher number of thousands will repeat 'n' and/or 't' and any number higher than 999,999 will repeat 'l' (as in million, billion, trillion, ...).
The largest number spelled without any repeating letters is "one thousand." Each letter in this phrase is unique, and it represents a significant value without any duplicates in its spelling. Other large numbers like "eleven" or "hundred" contain repeating letters, making "one thousand" the largest valid option.
makeup penman pneuma punkey unmake
hydro-pneumatic ambidextrously
ParticularProclaimed
juvenalostim
Walk my dog. :)
Without repeating, 4. With repeating, 8.
98765
98765432
uncopyrightable Dermatoglyphics misconjugatedly
9,876,543,210 9876543210
9875.