Figures show the average wait for a patient to see a specialist is 11 working days.
The Welsh Liberal Democrats have uncovered figures showing that Abertawe Bro Morgannwg UHB is routinely failing breast cancer patients.
There is Welsh Government guidance that a person suspected of having cancer should receive their first outpatient appointment within 10 working days of their initial referral.
However, an FOI request response from the health board shows that since 2013 5,176 patients have not received an appointment within 10 working days. The total number of referred patients was 7,194.
The longest a patient has had to wait until their first appointment was 207 working days, which was in 2013.
The figures show that the average wait for a patient to see a specialist is 11 working days.
The Labour Health Minister has previously stated that the "real key…is to make sure the everybody gets a first out-patient appointment within 10 working days of initial referral." He added: "I expect Local Health Boards to make that initial appointment within 10 days happen."
Peter Black, Assembly Member for South Wales West, said, "These figures are truly shocking.
"Being told that you may have breast cancer is of course an incredibly stressful time for any person. No-one should be waiting over two weeks until their first appointment. However it's clear that the vast majority of people, mostly women, are being forced to wait far longer than that.
"It's vitally important that patients suspected of suffering from cancer are seen promptly. Clearly, for many women that simply hasn't happened.
"Cancer causes one in four deaths in Wales, which is why the Welsh Liberal Democrats would appoint a National Cancer Director to fully implement a National Cancer Plan.
"For too long patients' views have been side-lined. Wales needs an NHS that puts patients first, and that's what the Welsh Liberal Democrats will deliver. We'll put patients' views front and centre to create an NHS that Wales deserves."