It's difficult to give you an answer, and it's not easy to understand what you mean by 'slowly', is the motor turning over slowly? or taking many turns before starting ?

I have had problems in the past with the HT Lead connection into the Coil, a little damp can make starting a longer process (the bike needs to turn over more before starting). Easily resolved by tightening the HT lead up and the application of some WD40 around the join.

If the power output from the battery isn't turning the motor fast enough, then you are right to look at the battery - 5 years is a good age for a battery anyway, and well worth the investment in a new one before your trip.

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Never underestimate the power of stupid people in large groups.