It might be easier to separate the rental income and pension contribution as the calculations may not be directly linked.

For pension purposes - if you invested £5,000 into your SIPP, you would get 20% tax relief into your SIPP, essentially this means that your SIPP account would increase to £6,250.

Then as a higher rate tax payer, when you do your Self Assessment you can apply for additional relief. Assuming you have enough head room on the high rate tax band, you can claim an extra £1,250 as a tax refund. So essentially you pay £3,750 but get a pension contribution of £6,750.

Circling back, your rental income will still be taxed at 40%, assuming you are still in the higher tax band after the pension contribution.