Swap letter and digit runs

Retina, 15 bytes

(\D+)(\d+)
$2$1

This replaces the regex (\D+)(\d+) with $2$1. Let's break that down if you don't know what that means.

The \D means 'match anything that isn't a number'. \d means 'match everything that is a number'. The + sign means 'match this at least once but try to match it as many times as possible'. The brackets define a group. The first group is (\D+) and the second is (\d+)

In the second line we say that we want to put whatever was matched by the second group, followed by whatever was matched by the first group. This effectively swaps the letter and digit runs.

Try it online!

Jelly, 9 bytes

~ṠŒg⁸ṁṭ2/

Try it online!

How it works

~ṠŒg⁸ṁṭ2/  Main link. Argument: s (string)

~          Apply bitwise NOT.
           Bitwise operators attempt to cast to int, so if c is a digit, this
           yields ~int(c), a negative number.
           If c cannot be cast to int, ~ will yield 0.
 Ṡ         Take the sign.
           We've now mapped digits to -1, non-digits to 0.
  Œg       Group consecutive equal elements.
    ⁸ṁ     Mold s as the result, grouping run of digits and runs of non-digits.
       2/  Reduce all pairs of runs by...
      ṭ        tack, appending the first run of the pair to the second run.

JavaScript (ES6), 34 bytes

s=>s.replace(/(\D+)(\d+)/g,"$2$1")

Try it

o.innerText=(f=
s=>s.replace(/(\D+)(\d+)/g,"$2$1")
)(i.value="uV5Pt3I0");oninput=_=>o.innerText=f(i.value)

<input id=i><pre id=o>