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If $5\%$ people said no then $95\%$ said yes.

Let $x\%$ be % of people who said yes to both. Then

$85\%$ + $75\%$ - $x\%$ = $95\%$ Then $x\%$ = $65\%$

Venn Diagram

95% said yes, so out of every 100 people, 95 said yes in all. Those who said yes to both lie under the set which is intersection of sets of people saying yes to question 1 and question 2 i.e. 75 and 85 respectively. Number of people in the required set is-
n(Intersection set)=n(Those saying yes to Question 1) + n(Those saying yes to Question 2) - n(Union of the two sets) = 75+85-95 = 65 for every 100 people meaning 65%

p(A)=75/100, P(B)=85/100, P(A'nB')=5/100 => P(AUB)'=5/100 =>1-P(AUB)'=P(AUB) . , 1-5/100=P(A)+P(B)-P(AnB)=>95/100=160/100-P(AnB) =>P(AnB)=65/100

Let the number of all people in the survey be 100 x

Number of people who said NO only to question 1 = 20 x

Number of people who said NO only to question 2 = 10 x

Number of people who said NO to both questions 1, 2 = 5 x

Then

Number of people who said YES to both questions 1, 2 = 100 x - 35 x = 65 x

The percent of people who said NO to both questions 1, 2 = 65 %

Suppose the total number of people surveyed is 100.

5 people said no to both questions. 25-5 = 20 people said no only to the first question 15-5 = 10 people said no only to the second question

100-(20+10+5)=65 people said yes to at least one of the questions

Let the number of people who said yes to the both questions be x

(75-20)-x = 55-x people said yes only to the first question (85-10)-x = 75-x people said yes only to the second question

55-x+x+75-x = 65 which gives x=65

Ans: 65

Let A be the probability of someone saying yes to both. Let B be the probability of someone saying yes only to 1. Let C be the probability of someone saying yes only to 2. Let D be the probability of someone saying no to both.

Since these are the only four possibilities, the total probability is 1 (100%). So A + B + C + D = 1 = 100% The remaining information gives us: A + B = 0.75, A + C = 0.85, D = 0.05,

Solving the system of linear equations (by any method you like) gives: A = 0.65, B = 0.10, C = 0.20, D = 0.05,

So the answer is A = 0.65 = 65%