As you will note by reading the RS book the majority of museums are free.
The popular sites such as Westminster Abbey., St Paul’s, Tower of London, Churchill War Rooms and the London Eye are not. Each have pricey admission fees.
Are all or any of these on the London Pass? Do the math.
I’ll surmise that touring with a 2 year old is a bit tricky attention span wise so you’ll need to have loose itineraries in case there needs to be nap time.
Thankfully given where you are staying you will have access to St James, Green and Hyde Parks where a 2 year old can enjoy waterfowl, dogs, Squirrels and horse back riders on a daily basis. Great spots to enjoy a picnic as well on sunny days.
Given u have 5 days and depending upon your interests u might consider training to Oxford or Cambridge. I suggest this not only because each town is interesting but you can then use your train ticket to get the 2 for 1 vouchers that Rick mentions in the book. Might be something to consider and if you were to decide to go get your train tickets well in advance to cut down on their cost.
Get the Oyster Card when u arrive. Pub grub is good and no one will blink an eye at the 2 year old at lunch time.
Checkout Mudchute Farm.
Make daily plans but be flexible.
Fabulous city. Have fun!