BACKGROUND: Estimates of immunity and severity for the SARS-CoV-2 omicron subvariant BA.5 are important to assess the public health impact associated with its rapid global spread despite vaccination. We estimated natural and vaccine immunity and severity of BA.5 relative to BA.2 in Denmark, a country with high mRNA-vaccination coverage and free-of-charge RT-PCR testing. METHODS: This nation-wide population-based study in Denmark included residents aged 18 years or older who had taken an RT-PCR test between 10 April and 30 June, 2022 (ie, the outcome period), and who the national COVID-19 surveillance system identified as having information since February 2020 on RT-PCR tests, whole-genome sequencing, vaccinations, and hospitalisation with a positive RT-PCR test and COVID-19 as the main diagnosis. First, we used a case-control design, in which cases were people infected with BA.5 or BA.2 during the outcome period and controls were people who tested negative for SARS-CoV-2 infection during the outcome period. We calculated the protection provided by a previous PCR-confirmed omicron infection against BA.5 and BA.2 infection and hospitalisation among triple-vaccinated individuals. Second, we compared vaccination status in people infected with BA.5 versus BA.2 and estimated relative vaccine protection against each subvariant. Third, we compared rates of hospitalisation for COVID-19 among people infected with BA.5 versus BA.2. We estimated effects using logistic regression with adjustment for sex, age, region, PCR-test date, comorbidity and, as appropriate, vaccination and previous infection status. FINDINGS: A total of 210 (2·4%) of 8678 of BA.5 cases, 192 (0·7%) of 29 292 of BA.2 cases, and 33 972 (19·0%) of 178 669 PCR-negative controls previously had an omicron infection, which was estimated in the adjusted analyses to offer 92·7% (95% CI 91·6-93·7) protection against BA.5 infection and 97·1% (96·6-97·5) protection against BA.2 infection. We found similarly high amounts of protection against hospitalisation owing to infection with BA.5 (96·4% [95% CI 74·2-99·5]) and BA.2 (91·2% [76·3-96·7]). Vaccine coverage (three mRNA doses vs none) was 9307 (94·2%) of 9878 among BA.5 cases and 30 581 (94·8%) of 32 272 among BA.2 cases, although in the adjusted analysis, there was a trend towards slightly higher vaccination coverage among BA.5 cases than BA.2 cases (OR 1·18 [95% CI 0·99-1·42]; p=0·064), possibly suggesting marginally poorer vaccine protection against BA.5. The rate of hospitalisation due to COVID-19 was higher among the BA.5 cases (210 [1·9%] of 11 314) than among the BA.2 cases (514 [1·4%] of 36 805), with an OR of 1·34 (95% CI 1·14-1·57) and an adjusted OR of 1·69 (95% CI 1·22-2·33), despite low and stable COVID-19 hospitalisation numbers during the study period. INTERPRETATION: The study provides evidence that a previous omicron infection in triple-vaccinated individuals provides high amounts of protection against BA.5 and BA.2 infections. However, protection estimates greater than 90% might be too high if individuals with a previous infection were more likely than those without one to come forward for a test for reasons other than suspicion of COVID-19. Our analysis also showed that vaccine protection against BA.5 infection was similar to, or slightly weaker than, protection against BA.2 infection. Finally, there was evidence that BA.5 infections were associated with an increased risk of hospitalisation compared with BA.2 infections. FUNDING: There was no funding source for this study.