Concept:
Mural traditions developed in different civilizations and periods.
To arrange them chronologically, we begin with ancient Egypt, then ancient Crete, Roman murals, early Christian or Byzantine murals, and later church mural traditions.
Step 1: Earliest murals.
Mastabas at Giza belong to ancient Egyptian funerary architecture.
So, the first is:
\[
D = \text{Murals at Mastabas, Giza}
\]
Step 2: Place Knossos.
Knossos in Crete belongs to the ancient Minoan civilization.
So, the second is:
\[
C = \text{Murals at Knossos, Crete}
\]
Step 3: Place House of Mysteries.
House of Mysteries at Pompeii belongs to Roman mural painting.
So, the third is:
\[
E = \text{Murals at House of Mysteries, Pompeii}
\]
Step 4: Place Classe, Ravenna.
Ravenna is associated with early Christian and Byzantine art.
So, the fourth is:
\[
A = \text{Murals at Classe, Ravenna}
\]
Step 5: Place St. Peter's Church, Rome.
St. Peter's Church, Rome belongs to a later Christian art tradition.
So, the last is:
\[
B = \text{Murals at St. Peter's Church, Rome}
\]
Thus, the correct order is:
\[
D \rightarrow C \rightarrow E \rightarrow A \rightarrow B
\]
Hence:
\[
\boxed{\text{(C) D, C, E, A, B}}
\]