Can I ask to perform the five daily prayers in Paradise, if I enter it by God's mercy?

Firstly: Jannah (Paradise) is a realm of recompense, not a realm of obligation, so there is no prayer therein.

Secondly: The idea of a servant yearning for prayer in Jannah is from the unseen, for which no evidence has been provided. Ibn al-Qayyim mentioned that acts of worship are lifted in Jannah, except for tasbih (glorification) and dhikr (remembrance), citing the Hadith in Sahih Muslim: "They will be inspired to glorify and praise [Allah] as they are inspired to breathe."