Does the above drop down - with icons and supporting message clearly demonstrates the priority levels?
Actually you do not have icons and supporting message because icons are supporting text message: icons alone are not clear enough to live without text.
In general icons need more active brain activity to be decodified than plain text unless it's a trivial standing-out symbol. Five icons with pretty arbitrary symbols aren't trivial enough and they're more decorative than useful.
If not, then what will be the better way to show priority levels consisting of 5 levels.
Drop icons and leave text. If context knowledge isn't enough to be sure users will understand what priority means then add some help. Five symbols are too many to be quickly recognized and scanned. Text and position in the list will play a more crucial role for users.
As side note: icon and color aren't useful in this case (because you have a dropdown with a small list) but same it's not true in other scenarios (tables, dashboards) where they both may help (it's material for another post but I'd reduce their number to three or less: low priority, high priority and critical).
Note that IMO priority doesn't match well with Trivial and an icon won't clarify this enough. What you're seeing is an aggregated index (a trivial to fix bug may have high priority because it happens 99.9% and users data will be corrupted). I think, in this case, proper wording is more important than icon with/without text message issue but decision is domain driven and shouldn't be generalized. Do you want to explicit that a trivial bug has low priority (because of any obscure company policy)? Write it, users won't need to guess or to interpret an icon:
- P1 Higher - blocker
- P2 High - critical
- P3 Normal - major
- P4 Low - minor
- P5 Lower - trivial
What I mean (I'm not sure it's clear) is that trivial is not a possible value for priority as 10 centimeters is not a possible value for hair color. However priority depends on other factors then if you label that box with priority you should (IMO) also provide proper priority values in your text.