Nope, that's how Provident work, which is why their APR is thousands.
OK there are different types of mortgage, but mainly they are interest only (used to be called an endowment) or repayment.
On an interest only mortgage you only pay the interest, you still owe the same amount at the end as you did when you first took out the mortgage.
Back in the 1970s these were sold alongside an 'endowment' so your mortgage payment paid the interest but then you paid into an endowment which was invested for you. When the mortgage came to an end the endowment was used to pay off the debt and hopefully you also had a chunk of cash left over.
But then in the 1980s endowments didn't pay enough to clear the debt, and house prices dropped so even if you could sell you didn't have enough money to pay the debt so were left in debt and homeless.
These still exist but without the endowment part, so say you are 20 years old and your gran left you £500 000 in trust that you will get when you are 30. It could be worth getting an interest only mortgage so you don't pay as much each month but you know you will be able to pay a debt of £500 000 in 10 years.
The other main type is a repayment mortgage.
The money you pay every month is paid towards the interest and the amount loaned. So using your example:
5% of £100,000 = £5,000 - this is true, but only for the first month, your payment is towards the interest and the loan, so say you pay 100 off the loan and the rest is interest the next month the interest is:
5% of £99 900 =£4995
So say the rate stays at 5% and you over pay the amount you actually owe goes down quicker than the £100 a month your contract says you pay.
Now that's a simplified version because you often also pay a life insurance policy in case you die.
So the amount you pay is:
Part towards the loan+ interest + life insurance