ok, solo hay que poner el sum afuera del case...
Código:
SELECT pr.Nombre, Count(CodPedido) as 'Pedidos Total',
SUM(CASE pr5.IvaSiNo WHEN 1 THEN pr5.Importe Else 0 END) as totalcon,
SUM(CASE pr5.IvaSiNo WHEN 0 THEN pr5.Importe Else 0 END) as totalsin
FROM gesberna_pedidos pr5
INNER JOIN gesberna_clientes pr ON pr.CodCliente = pr5.CodCliente
GROUP BY pr.Nombre

Saludos!