Hey there @tcspears - great topic! Thanks so much for sharing.
So what you have going on here could be due to a few things.
Firstly - what kind of event type is this event? I ask because, for example, if you are seeing no option to “reschedule” on certain other event types I will assume those are One-Off Meetings or bookings made through Meeting Polls - neither of which can be edited, changed or officially rescheduled once invitees select and book their times. However, all of your regular event types (one-on-one, Collective, Group, Round Robin) should have a “reschedule” option next to each booking under your “scheduled events” tab.
Secondly - there are a few reasons you could be missing that 5pm time slot on the date/time you’d like to reschedule this group of invitees. You can use our Troubleshooting availability tool on your scheduling page in order to understand what's causing a conflict in your schedule. I find it to be super helpful and it resolves most availability issues. 
Check that out to see what reason is given on that date/time and go from there. You can read more about using this tool and how to troubleshoot your availability/come to a solution in the article I’ll link at the bottom of this reply!
Thirdly - while there is no workflow that will allow for you to reschedule your invitees, you can still avoid emailing them to make them sign up again. You’ll want to cancel the desired time slot - then take all of the invitee details from your “scheduled events” tab, head to your booking page - and book each of the 5 invitees yourself, as though you are them, by entering all of their info. I know this isn’t the prettiest solution but it’ll work and should take about five minutes!
I hope this helps - but let me know if you need further clarification!
The promised article:
Thank you. These are Group events where they click into a round-robin, and will get load balanced between me and a colleague.
I have my schedule set to only allow 6pm EST to 7pm EST on Mondays and Tuesdays, my colleague’s is pretty variable I think.
I did create a timeslot from 5pm to 6pm on the day in question, but even then when I go into the meeting, it doesn’t show the reschedule option. I tried the Troubleshooting tool, and it shows the availability correctly. I’ll check with the person who setup the events, maybe these are one-off meetings, and that’s why?
Hey there, again, @tcspears - thanks for answering!
I am assuming because there are two hosts assigned, it’s actually a Round Robin! This also means it is not a one-off meeting, as that’s a separate event type itself, too!
The reason this could be happening? The settings in place for distribution between hosts. The two options are as follows:
Optimize for availability - allows invitees to book meetings whenever a host is available. Use this to maximize the number of potential meetings booked and when the even distribution of meetings across hosts is less important.
Optimize for equal distribution - allows for the most even distribution of meetings across hosts. This can lead to fewer booked meetings overall as equal distribution is given priority over host availability.
Click “show content” to learn more about each of these options, below!
How does "optimize for availability" work?
When optimizing a round robin event for availability, Calendly will show times on the calendar when 1 person or more is available. If multiple people are available, this is where the priority star setting will come in. Here are a few key things to know:
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Calendly will only assign the meeting to an available teammate.
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Calendly will assign the meeting to the team member with the highest Calendly priority relative to other available teammates first.
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If there is a tie, then the person that has not been scheduled recently is chosen.
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If a tie remains, then someone will be randomly chosen.
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The priority of each team member can be easily adjusted using the priority stars on the event type.
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If team members have equal priority, Calendly will assign the meeting to the least recently scheduled person for this event type.
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If team members tie on priority and least recently scheduled, the meeting is assigned at random.
How does “optimize for equal distribution” work?
With this setting, Calendly will monitor how many meetings for a round robin event are booked with each individual. Calendly will then compare the teammates' meeting counts.
If someone on your team is at least three meetings ahead of other teammates, their availability will be turned off until other team members catch up.
When optimizing a round robin event for equal distribution:
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No team member can be more than three meetings ahead.
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If you add or remove people from a round robin event, this will reset the distribution algorithm and start every member at 0.
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If a team member is three meetings ahead, that team member cannot be booked until other teammates are scheduled.
Example: If Jim has 3 meetings and Karen has 0 meetings, Calendly will remove Jim's availability until Karen has 1 meeting. Now Jim's available time slots will again show on the booking page. If Jim is scheduled again and the relative count returns to +3 (4 to 1), Jim's availability will again be removed.
Calendly compares meeting counts for the period of time that all current hosts are on the event type together. This means that if a team member is added or deleted from an equal distribution event, the algorithm will treat the team member as if no meetings have been booked with them. If you have an event type where hosts are regularly being added or removed, this might cause inconsistencies with distribution.
Use the Admin View at anytime to troubleshoot why you or your team member is unavailable. The error “UNFAIR” shown below is due to unequal distribution:
What if I switch from "optimize for availability" to "equal distribution" (or vice versa)?
Changing the setting will take effect immediately. The next booking will interpret the round robin availability based on that new setting. Calendly won't consider previous settings or scheduled meetings counts.
Reporting on meeting distribution
For more information on how to download an activity report for a round robin event, please check out the article on how to export a list of team event type activity.
...PHEW! Now that you understand how that all works, go ahead and look at your RRET and see what settings are in place. For example, if you’ve opted for “equal distribution,” even if you are available for a time slot, it can be blocked off if the “fair” rule is in place (if you have too many bookings compared to the other host).
I hope this helps!
@tcspears - one more thing!
A Round Robin Event Type cannot be a Group Event Type, nor can it be a One-Off Meeting (you can click each of these links to read about the differences in each event type!).
I just wanted to clarify for you. This way, you know what kind of event type you have created. We also have a Collective Event Type which allows for multiple hosts at the same time to meet with a single invitee in a time slot.
Lastly - bookings already made will not be changed when you update your event type settings/availability. I hope this helps!
