Both parties will receive the full written reasons from the independent regulatory commission that imposed the suspension - the minimum ban for an aggravated offence under the FA's rules.
West Brom striker Anelka is able to appeal against the ban, but the FA is also permitted to appeal to try to have the ban increased.
FA general secretary Alex Horne said: "This was a gesture we haven't seen before in English football. The reality is we haven't got the written reasons yet, we will get those on Monday at which point it is open to appeal from either our side or Nicolas Anelka's side so I can't comment personally as to whether five matches are enough."
The quenelle salute has anti-Semitic connotations in Anelka's home country of France, but the commission accepted there was no intent by West Brom striker to be anti-Semitic. Under strict liability rules, however, he was found guilty of an aggravated offence.
New rules brought in this season mean any racial or discriminatory offence carries a minimum five-match ban, and FA chairman Greg Dyke said the governing body would look to see if these changes had been effective.
Speaking after the International FA Board meeting in Zurich, he said: "This is an evidence-based inquiry and what did Mr Anelka say and what was basis for the decision - we will see that on Monday.
"We will look at the whole thing again once this one has been done. This was not an easy case, because for most people in England that sign meant nothing.
"It's only what it meant in France that became important, so I we will look at the judgement and will ask people do we think that's fair or that we should change anything as a result of that."
Anelka performed the gesture as a goal celebration after scoring in his club's match against West Ham on December 28.
Anelka insisted the salute was in support of his friend, the French comedian Dieudonne M'bala M'bala, the person who first brought the quenelle to prominence. Dieudonne has been prosecuted for anti-Semitic offences and has been barred from entering the UK.
UEFA is holding a disciplinary hearing on Monday into the case of a Belgian futsal player Omar Rahou who also made a quenelle gesture during a match. UEFA's new racism rules carry a minimum 10-match ban.