imc

Let the pizza have $60$ slices, since the least common multiple of $(5,3,4)=60$. Therefore, Alex ate $\frac{1}{5}\times 60=12$ slices, Beth ate $\frac{1}{3}\times 60=20$ slices, and Cyril ate $\frac{1}{4}\times 60=15$ slices. Dan must have eaten $60-(12+20+15)=13$ slices. In decreasing order, we see the answer is $\boxed{\text{Beth, Cyril, Dan, Alex}}$.