re: design notes
@rey a final note: while you can do this with what you have already (though i would want to run the numbers on power dissipation in the 4401/4403s, they're not rated for all that much), my personal recommendation would be to use something more along the lines of the DMG2302 https://www.digikey.com/en/products/detail/diodes-incorporated/DMG2302U-7/2192636 and DMP2215 https://www.digikey.com/en/products/detail/diodes-incorporated/DMP2215L-7/1774204
both of those should have near-zero power dissipation except when switching (less than 100 mΩ of on-state resistance and no saturation voltage like bjts have) so they wouldn't even get close to warm, and you'd have nearly the full 5 V on the output
the only problem is that they're SOT-23; you may be able to make that work with some stripboard though! i've used some surface mount parts on stripboard before, though never sot-23s
-F