Hi John,
If it is the correct web site for your charger that Duke linked to, the charger supplies a maximum of 500mA. I have not looked at how it decides that the battery is fully charged, but the chances are that you should be able to put any compatible chemistry cell, into the charger, and it will charge it. For your hypothetical 5Ah battery situation, if there is a timer in the charger, it may not fully charge the battery, also the charger may have other checking circuits. Some of those aspects are mentioned in the link I quoted.
The question then becomes one of how much effort I or others are prepared to put into researching the construction and operation of the charger, (and in trying to decide exactly what your hypothetical battery may be) and as far as I'm concerned, unless persuaded otherwise, this is about as far as I'm going in an open forum situation. The link was to give you some background to batteries/chargers, so that you could make your own guesses a bit better, and understand that for others to give a precise answer to your question may depend on information that you have not supplied. So, if I say 'yes, it will work fine', and then next week it goes to smoke, then you will blame me. If I say 'no-way' (the safe option), then someone will try it, and find it works just fine.
I can say, however, that _my_ hypothetical 5Ah battery will work fine in your charger ;-).
Best wishes,
Ray