Five days after a hair transplant: did I screw everything up?

You haven't done anything wrong.  It is expected to have the scabs fall out with the hair.  As long as there is no bleeding the follicles are safely implanted.  Don't be overly aggressive with trying to get the scabs off.  Just allow them to fall out over time.

An FUE is treated just like
a regular hair transplant with regard to the recipient area, but the donor area
has open wounds which require daily washing with soap and water. Within 3 days
of surgery, you can resume full activities, heavy exercises if you wish. The
recipient area requires daily washes as well to keep the recipient area free of
crusts. I generally recommend the use of a sponge and supply my patient with a
surgical sponge to fill with soapy water and press on the recipient area daily.
By repeating this daily, all crusts can be washed off without any fear of
losing grafts. IF any crust are present, use a Q tip and dip it into soapy
water, and roll it on the crusts and that will lift them off without dislodging
them, but never rub them, just roll the Q tip on the recipient crust. I like to
see no evidence of any crusting in the recipient area and the crusts from the
donor area gone in 7-10 days with daily washing,.