The LIKE operator in MySQL is not that versatile I'm afraid. There are a number of alternatives you can sue though:
select COALESCE(sum(payable_amount),0.00) from billing where bill_date = '2013/12/05' and pay_mode = 'Cash' AND ASCII(invoice_no) in (65,66,67,68,69)
or
select COALESCE(sum(payable_amount),0.00) from billing where bill_date = '2013/12/05' and pay_mode = 'Cash' AND LEFT(invoice_no, 1) in ('A','B','C','D','E')
Both of these will only match against the uppercase characters - you'll ned to add the relevant codes if you want to match lowercase as well.
There is also the REGEXP function, but damned if I can understand it ro get it to work,,,
http://dev.mysql.com/doc/refman/5.0/en/regexp.html#operator_regexp[
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