plouffe13,
Welcome to JOF
In 2005 Jayco used both the TPO (thermo plastic) and EPDM (rubber) roofing materials, it varied with the different models (FW, TT, HTT, etc.). The TPO material had a rough textured feel to it's top surface, the EPDM had more of a smooth surface feel.
My original TPO material on my 2005 Eagle had a "fleece" backing, not rubber. I had my TPO replaced with EPDM a couple years later under warranty due to issues with a roof/side wall leak.
It's possible if you purchased your 2005 trailer used it may have been replaced with a EPDM material, or the manual was in error due to the two different materials used back then.
Remove the plastic A/C grill from the interior ceiling, there should be some excess roofing material there that you can confirm if it's TPO (look for the fleece backing).
Bob
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2016 GM 2500HD 6.0L/4.10
2018 Jay Flight 24RBS
2002 GM 2500HD 6.0L/4:10 (retired)
2005 Jayco Eagle 278FBS (retired)
1999 Jayco Eagle 246FB (retired)
Reese HP Dual Cam (Strait-Line)