Possibility of using a drop-down time selector instead of a calendar

I'm wondering if it's possible to have a drop-down selector (or possibly a div with scrollbar?) for clients to select a start time for their session?

The reason is that my client has a minimum session time of 5 minutes so the calendar that displays the open/unavailable time slots is incredibly long and awkward since it's in 5 minute increments. I'm thinking that a drop-down would let the client scroll down to select their start time.

Secondly, is there a way to just display a start time only, and not an incremental time, when showing available time slots? The reasoning is that, in addition to 5 minute sessions, she also offers 15/30/45/60 minute sessions. The calendar displays only 5 minute slots, so 3:00 - 3:05pm, for example, which is confusing people wanting to book the longer sessions (to them it looks like just 5 minute time slots are offered). If it simply showed a start time, like just 3:00pm, 3:05pm, 3:10pm, it would make sense to them.

Lastly, thanks for any suggestions anyone has that will make this calendar work out for my client. The 5 minute session is really throwing me for a loop on how to have the open/closed time slot calendar show up so it's not taking up 5 scrollable pages. I'd like to get it figured out for them right away so they can launch the site.