Sliding from 3 to 5 and then hitting 2? Do I need to stretch my hands that much? Or is this made unnecessarily hard?
Not at all (if you don't have a ultra-small hand).
My advice would be to play it just as it is written. The reason is that as you play more and more, your hand will be progressively more able to stretch, so after some time, you will be absolutely OK with it.
On top of that, stretches like this just occur quite frequently on the guitar (they often arise when you try to play a bass line independent of your melody), and often they are far worse. Because of that, it's no use trying to avoid or work around them -- you will hit another one sooner or later. (For instance, you can get a very useful G major "shape" if you stop the low E at the 3rd fret and the high E at the 7th (or even 10th) fret.)
There is a crucial piece of information missing from this TAB. What fingering is suggested for this? If you slide using the ring finger (or pinky) your index will be free to grab the 2nd fret and should not be a problem. Whether or not that seems reasonable depends on the notes before the 2 you've shown.
If you really want help please post the entire line so we can see how this phase fits into the bigger picture. As some have mentioned the thumb is also an option.
As written it's a somewhat difficult passage. The performance is much clearer when you consider the standard notation: the A on the first string has to be held until you hit the B note tabbed on the sixth string later in the measure.
Since the B is two frets higher than the A, you'd need to do the slide with your ring finger, then reach a bit with the index finger to barre the 2nd fret for the E, A, and C# notes. You'd then have to continue holding the A while you stretch to play the 6th string B with your little finger. It's a bit awkward.
This is a good example of how tab shows you only ONE way to do something, and an alternative might make more sense. I'd probably make the slide with the little finger, and then play all of the next notes on the 2nd fret with an index finger barre, playing the B on the 5th string, then moving to 7th position for the next beat and a half.
Assuming it's correctly noted, it's a good exercise - one of the biggest differences between pros and amateurs isn't whether they play the notes in the right place... it's whether they hold the notes for the right length.