I just came across this problem recently. According to RFC 5424, the Syslog message should be in the following format: HEADER SP STRUCTURED-DATA [SP MSG], where SP is a space character and the brackets represent the data is optional. Having said that I found it easier to break the message down into three separate regular expression patterns and then combine them when I instantiate a Regex object for comparing.
Here's my sample class. I hope it helps.
public class SyslogMessage
{
    private static readonly string _SyslogMsgHeaderPattern = @"\<(?<PRIVAL>\d{1,3})\>(?<VERSION>[1-9]{0,2}) (?<TIMESTAMP>(\S|\w)+) (?<HOSTNAME>-|(\S|\w){1,255}) (?<APPNAME>-|(\S|\w){1,48}) (?<PROCID>-|(\S|\w){1,128}) (?<MSGID>-|(\S|\w){1,32})";
    private static readonly string _SyslogMsgStructuredDataPattern = @"(?<STRUCTUREDDATA>-|\[[^\[\=\x22\]\x20]{1,32}( ([^\[\=\x22\]\x20]{1,32}=\x22.+\x22))?\])";
    private static readonly string _SyslogMsgMessagePattern = @"( (?<MESSAGE>.+))?";
    private static Regex _Expression = new Regex($@"^{_SyslogMsgHeaderPattern} {_SyslogMsgStructuredDataPattern}{_SyslogMsgMessagePattern}$", RegexOptions.None, new TimeSpan(0, 0, 5));
    
    public int Prival { get; private set; }
    public int Version { get; private set; }
    public DateTime TimeStamp { get; private set; }
    public string HostName { get; private set; }
    public string AppName { get; private set; }
    public string ProcId { get; private set; }
    public string MessageId { get; private set; }
    public string StructuredData { get; private set; }
    public string Message { get; private set; }
    public string RawMessage { get; private set; }
    /// <summary>
    /// Parses a Syslog message in RFC 5424 format. 
    /// </summary>
    /// <exception cref="FormatException"></exception>
    /// <exception cref="OverflowException"></exception>
    /// <exception cref="ArgumentNullException"></exception>
    /// <exception cref="InvalidOperationException"></exception>
    public static SyslogMessage Parse(string rawMessage)
    {
        if (string.IsNullOrWhiteSpace(rawMessage)) { throw new ArgumentNullException("message"); }
        var match = _Expression.Match(rawMessage);
        if (match.Success)
        {
            return new SyslogMessage
            {
                Prival = Convert.ToInt32(match.Groups["PRIVAL"].Value),
                Version = Convert.ToInt32(match.Groups["VERSION"].Value),
                TimeStamp = Convert.ToDateTime(match.Groups["TIMESTAMP"].Value),
                HostName = match.Groups["HOSTNAME"].Value,
                AppName = match.Groups["APPNAME"].Value,
                ProcId = match.Groups["PROCID"].Value,
                MessageId = match.Groups["MSGID"].Value,
                StructuredData = match.Groups["STRUCTUREDDATA"].Value,
                Message = match.Groups["MESSAGE"].Value,
                RawMessage = rawMessage
            };
        }
        else { throw new InvalidOperationException("Invalid message."); }
    }
    public override string ToString()
    {
        var message = new StringBuilder($@"<{Prival:###}>{Version:##} {TimeStamp.ToString("yyyy-MM-ddTHH:mm:ss.fffK")} {HostName} {AppName} {ProcId} {MessageId} {StructuredData}");
        if (!string.IsNullOrWhiteSpace(Message))
        {
            message.Append($" {Message}");
        }
        return message.ToString();
    }
}