Step 1: Total time from 10:00 AM to 1:27 PM
\[
= 3 \, \text{hours and} \, 27 \, \text{minutes} = 207 \, \text{minutes}
\]
Step 2: Total rest time
After 4 sessions, rest happens 3 times:
\[
\text{Rest time} = 3 \times 5 = 15 \, \text{minutes}
\]
Step 3: Total teaching time
\[
207 - 15 = 192 \, \text{minutes}
\]
Step 4: Duration per session
\[
\frac{192}{4} = \boxed{48 \, \text{minutes}}
\]