Probability question about combining outcomes with variable likelihoods

I'm having trouble sorting out a problem. Let's say I have 5 fair coins and 2 six-sided dice. The coins have a star on one side, and the other side is blank. The dice have stars on 5 faces, and a blank on the remaining face.

Individually, each coin has a 1/2 chance of showing a star, and each die has a 5/6 chance of showing a star.

What is the probability of flipping/throwing the dice all at once and seeing at least 4 stars.

There are 1152 possible outcomes (2*2*2*2*2*6*6). If the solution only involved coins, I'm able to figure it out, but the addition of the dice is making my head hurt haha. Thanks for anyone who can help.