Run each claim through what we know about gut neuroendocrine tumours and find the odd one out. Carcinoids favour the GI tract, behave indolently, and have characteristic site and sex patterns.
Small bowel plus appendix making up roughly 60% of GI carcinoids fits the classic distribution, so that statement holds. The greater-than-60% five year survival also fits, because these are slow, well-differentiated tumours with a generally favourable outlook. The female excess of appendiceal carcinoids is a recognised teaching point as well.
That leaves the claim that the rectum is spared. This is plainly false: the rectum is in fact a leading site for carcinoids and they are often found by chance during colonoscopy or proctoscopy. Because the rectum is commonly involved rather than spared, this is the incorrect statement the question is hunting for.
$\text{small bowel + appendix} \approx 60\%,\; \text{5-yr survival} > 60\%$ are correct; rectum is NOT spared.
\[\boxed{\text{Rectum is spared}}\]