Sometimes low blood pressure isn't the issue but the side effect.
I agree.

Did your doctor check your Iron levels?
A low BP can be the sde effect of Abnormal Iron levels but mostly an indication of anaemia. remember you now have 2 'people' to supply blood to (one for you and one for bubba) so it is fairly common to have low bp in early pregnancy.
Increasing fluids gives you more volume in your blood so your heart pushes greater amounts through your body- but its sound like you are having more than sufficient amounts. Actually 5 litres is huge if you are doing it because you are thirsty- have you been checked for diabetes?
Maybe get your iron levels checked but meanwhile try a iron supplement like Elevit...and avoid caffeine and caffeine inhibits the absorption of iron...

Otherwise everyone here has given you great advice