JSONPath is not suitable for what you are trying to achieve: JSONPath is designed to select values and not key-value pairs. What you want could be achieved with Jackson or any JSON parser for Java.
If you want to go for Jackson here's the code that will do the trick:
String json = "{\"a\":1,\"b\":2,\"c\":3,\"d\":4,\"e\":5}";
ObjectMapper mapper = new ObjectMapper();
JsonNode tree = mapper.readTree(json);
ObjectNode node = mapper.createObjectNode();
node.set("b", tree.get("b"));
node.set("d", tree.get("d"));
node.set("e", tree.get("e"));
String result = mapper.writerWithDefaultPrettyPrinter().writeValueAsString(node);