Yes, need a picture of the mock orange. In your zone, I would do both in the spring.

Do you mean choisya? I give mine a tidy-up chop as soon as the first flush of flowers have finished. But I generally always prune evergreens around this time (July-ish).

We sometimes refer to philadelphus as mock orange...and if this is the same for you, then definitely cut back the flowering shoots immediately after blooming as they flower on older wood so need a year to lengthen and ripen the wood for following years blossom.

Cheers, campanula/rosa

Couldn't state with certainty what would be your best option for the hardy hibiscus.

Mock orange - Philadelphus - like all spring flowering shrubs is best pruned immediately after flowering so as to maximize the next season's flowering potential.

I would consider the cusp of November a bit too late in the season to be transplanting perennials in your location. It is even for me :-)) I'd also wait until spring to move the hibiscus as well.

There are various cultivars of Philadelphus. Some are large shrubs but others are quite compact. There are single and double flowers and some lack the fragrance. As GG said, prune after flowering. If it needs it. Yours is young so you could just leave it alone.

Is the hardy Hibiscus H. syriacus or H. moscheutus?

Nb Choysia would be doubtfully hardy in z5.

ETA now we have pix it's H. moscheutus. Also, for most Philadelphus cultivars that bed will soon prove rather small and you could end up hacking it back regularly.

The hardy hibiscus I want to transplant has dinner plate size flowers and is a H. moscheutus.

Our mock orange is supposed to be a compact variety.

I just managed to post pictures