Answer

In 2005, Digambar Paryushan, also commonly called Das Lakshan Parva, started on:

September 8, 2005.

Explanation

In the Digambar Jain tradition, Paryushan is observed as Das Lakshan Parva, a 10-day spiritual festival focused on the ten supreme virtues:

• Uttam Kshama — supreme forgiveness
• Uttam Mardav — supreme humility
• Uttam Arjav — supreme straightforwardness
• Uttam Shauch — supreme purity/contentment
• Uttam Satya — supreme truthfulness
• Uttam Sanyam — supreme self-restraint
• Uttam Tap — supreme austerity
• Uttam Tyag — supreme renunciation
• Uttam Akinchanya — supreme non-possessiveness
• Uttam Brahmacharya — supreme celibacy/chastity

Takeaway

So, Digambar Paryushan / Das Lakshan Parva in 2005 began on September 8, 2005.