Orthotics for walking/running and cycling are totally different
You probably should not wear your walking/running orthotics for cycling. Cycling and running/walking orthotics are made different because the needs of your feet are different when walking and cycling. I'm not sure what your issues are, i.e. pronation?, shorter leg? whatever, but if you need orthotics on the bike, you should get specific orthotics for the bike.
Why not try the shoes without the orthotic for one ride and see what happens. You should have some sort of small insert however. If your shoes did not come with one, you should cut one to size from an old gym shoe or buy one at the store.
You will soon find out if you need an orthotic for riding but I would try it without. My husband has a short leg and his feet pronate pretty badly. When he was racing in his 30's-40's doing lots of mileages and repetition, he would get knee tendinitis and very, very tight Iliotibial bands (this is common with most cyclists). He went to a special guy who does cycling orthotics, they looked at him on the bike (videoed him) and determined what to do with his orthotic to make him comfortable and it worked!
Now that he does not ride quite as much nor as hard, he does not wear the orthotics and seems to be fine. I think it is also because he is so used ot cycling now too, but that is my theory.
More about my feet and the rest of me, too!
Yes, I can do pretty much anything without foot pain (besides wear the damn bike shoes) as long as I have my orthotics in. I can't answer the 5k question, though- I don't run at all and haven't for years, I'm quite overweight and have back issues plus no ACL in one knee, so if I ran, that would probably be the end of me. My other challenge with club riding is that I have super strong legs, so I'm usually out in front on flats/slight inclines, but the hills (and I live in the Bay Area) are very challenging for me, because I'm about 60 pound overweight and have a very heavy hybrid (not that I think that makes a bit of difference- my bike is maybe about 5 lbs heavier than everyone else's, but the real issue is the surplus 60 lbs on my body. I'm working on that....