Final answer:
The letter style with indented new paragraphs is often known as modified-block or semi-block, but in business letters, block formatting is typically used with paragraphs starting at the left margin.
Step-by-step explanation:
The letter style in which the first line of each new paragraph is indented 5 spaces is commonly known as the modified-block or semi-block letter format. However, in business letters and academic writing, this style is less commonly used. Instead, the block format is preferred, where each paragraph begins at the left margin without any indentation. For quotations in an academic context, block quotations are used when the quotation is more than four lines, and these are also indented but maintain the same line spacing as the rest of the text.