Included both horizontal spaces (after heading number) and spacing before and after titles without using sectsty. Change the formatting commands in \titleformat as required and the horizontal spacing between the number and heading.
\documentclass{article}
\usepackage{lipsum}
\usepackage{titlesec}
\usepackage[T1]{fontenc} % EDIT - allows multiple font styles %
% Change horizontal space in titles here
% [block]{Formatting command}{Put `the' in front of paragraph etc}{Space after number}{}
\titleformat{\section}[block]{\large\scshape\bfseries}{\thesection.}{0.2em}{}
\titleformat{\subsection}[block]{\large\scshape}{\thesubsection}{0.3em}{}
% EDIT - to show the multiple font styles being applied due to package fontenc
\titleformat{\subparagraph}[block]{\scshape\bfseries}{\thesubparagraph}{0.3em}{}
% Change vertical space \beforetitle and \aftertitle here, as above use \subparagraph etc.
% 0pt is how far from the left margin the entry is placed
\newcommand\aftertitle{2ex}
\newcommand\beforetitle{0.7ex}
\titlespacing{\section}{0pt}{\aftertitle}{\beforetitle}
\titlespacing{\subsection}{0pt}{\aftertitle}{\beforetitle}
\titlespacing{\subsubsection}{0pt}{\aftertitle}{\beforetitle}
\titlespacing{\paragraph}{0pt}{\aftertitle}{\beforetitle}
\titlespacing*{\subparagraph}{0pt}{\aftertitle}{\beforetitle}
\setcounter{secnumdepth}{5}
\begin{document}
\section{Section}
\lipsum[1]
\subsection{Subsection}
\lipsum[2]
\subsubsection{Subsubection}
\lipsum[3]
\paragraph{Paragraph}
\lipsum[4]
\subparagraph{Subparagraph}
\lipsum[5]
\end{document}
How it looks (EDIT - updated to include fontenc package for subparagraph formatting):
