Chris, there's thiosulfate in KRST, so a washing aid will help to remove it, after toning. I don't have any experience of TF 5, however, so I cannot judge its ability to convert the complex less-soluble byproducts of fixing (argentothiosulfates) to those that wash out more easily. In general, for what I know, those are not an issue if your fixer is quite fresh, and they become an issue when it is exhausting, while the 2nd fixer, being still fresh, is able to work on them. Two things make it more complex, however: KRST has thiosulfate, and so I expect it might help to convert the insoluble argentothiosulfates into the more soluble ones, and a good washing aid helps remove them faster than just water, as long as it is fresh and potent, that is the sodium sulfite has not oxidised yet.
My suggestion would be to include a washing aid in your process, and to test for residual thiosulphate after the washing to establish the correct duration for your conditions, temperature, washer type, and water hardness.
A simple washing aid, following Anchell:
Water (125F/52C) 750 ml
Sodium sulfite 200g
Sodium bisulfite 50g (Achell writes this is of more importance for film and can be skipped for paper to improve gloss)
Water to make 1 liter
This makes stock, dilute 1+9 to make working solution. If you don't work often and prefer not to keep stock solutions for long, you can just mix the working strength wash using 20g sodium sulfite in 1l water.