The Mishna in Pesachim 1:5 says (Open Mishna translation):
וְעוֹד אָמַר רַבִּי יְהוּדָה, שְׁתֵּי חַלּוֹת שֶׁל תּוֹדָה פְסוּלוֹת מֻנָּחוֹת עַל גַּג הָאִצְטַבָּא. כָּל זְמַן שֶׁמֻּנָּחוֹת, כָּל הָעָם אוֹכְלִים. נִטְּלָה אַחַת, תּוֹלִין, לֹא אוֹכְלִין וְלֹא שׂוֹרְפִין. נִטְּלוּ שְׁתֵּיהֶן, הִתְחִילוּ כָל הָעָם שׂוֹרְפִין. רַבָּן גַּמְלִיאֵל אוֹמֵר, חֻלִּין נֶאֱכָלִין כָּל אַרְבַּע, וּתְרוּמָה כָּל חָמֵשׁ, וְשׂוֹרְפִין בִּתְחִלַּת שֵׁשׁ:
Rabbi Yehudah also said, "Two loaves of bread of a thank-offering [that had become] unfit were placed on the roof of the [Temple] portico. As long as they [both] lay [there], all the people would eat [chamets]. [When] one of them was removed, they would suspend and neither eat nor burn [their chamets]. [When] the second one of them was removed, all the people would begin burning [their chamets]." Rabban Gamliel says, "[Chamets that is] chulin [ food permitted for general consumption] may be eaten through all [the first] four [hours of the day]; but [chamets that is] terumah [may be eaten even] through all [the first] five [hours of the day]; and we must burn [all chamets] at the beginning of the sixth [hour]."
Are we to understand this line of the Mishna as saying that we are not required to burn our chametz during the fifth hour, or should we understand it as saying that we cannot burn it during the fifth hour? Perhaps it would be forbidden to burn chametz during the fifth hour because of an issue of bal tashchit, or it's possible that doing this would confuse the erev Pesach schedule and thus confuse the people as well.
If there are interpretations that this is forbidden, where do people in these times get permission to burn their chametz early?
