From terminal 5 to terminal 3 at Heathrow

90 minutes sounds right for the minimum connection time that airlines consider appropriate for a single ticket where you aren't collecting bags. You ought to do it somewhat less than that taking the airside connection. Note that you will still have to go through security on arrival at terminal 3 airside, as the transfer is mixed domestic and international flights arrivals. If you had been on a BA flight from T5 you would have gone straight into the departure part of the terminal without a further check.

Twenty minutes sounds more like a typical journey time only, either landside or airside.

As long as your plane lands on time, 2 hours is fine.

As Marco said, 90 minutes is the minimum connection time (meaning an airline won't offer a connection with less than 90 minutes to connect). You have 30 minutes more than the MCT.

It does not take that long to transfer from T5 to T3 when you stay airside. Just follow the signs for flight connections.

Have made that same connection a few times. 40 - 45 min is about the usual, but have done it in under 30 min once. The signage is easy to follow and the bus system has been very efficient, so do not worry if it seems like a lot of people are in line. You should have plenty of time even if the first flight is a few minutes late.

Here is the Heathrow Airport website's excellent connection tool. Put in all the details of your flights, and it will show you all the steps and estimated times: http://www.heathrowairport.com/heathrow-airport-guide/flight-connections/connection-guides