To choose the correct word, we need to look at the grammatical structure and the logical meaning of the sentence:
Grammatical Structure (The Participle Phrase): The sentence already has a main verb ("left").
"Artists like Leonardo da Vinci and Michelangelo left an incredible mark..."
To connect the next part of the sentence smoothly, we need a present participle (-ing form). This functions as a participle phrase describing the result or the ongoing action of the artists' "mark." "Influencing" fits this structure perfectly.
Logical Meaning: The passage discusses the long-term impact of Renaissance artists. To "leave a mark" implies that their work had a lasting effect on others. Influencing means having an effect on the character, development, or behavior of someone or something—in this case, "art."
Contextual Clue: Blank number 5 is followed by "centuries," which suggests a long-term impact. "Influencing art for centuries" is a standard and logical expression in art history.