How do I compute the +5 charge state m/z for a peptide of 3751.0 Da?

Concretely: +5 · 3751.0 Da.

I want the working, not the result — I need to be able to redo it with different numbers.

I care about the precision as well as the value — I want to know how many figures are real.

How many significant figures are actually justified here?

Stated carefully, the single most important fact about mass spectrometry for peptides is that it measures only the molecular weight and tells you almost nothing about whether the peak is actually your target.

The charge state distribution depends on the solution pH, the structure of the peptide and the source conditions, so the same peptide can look different under different conditions.

The m/z accuracy achievable depends on the mass analyser type — quadrupole gives low accuracy, time-of-flight gives moderate accuracy, and Orbitrap gives high accuracy.

I would not trust a mass result without a good baseline and a blank injection check.

A correct mass is necessary for identity but not sufficient — you also need the chromatography to confirm it.

Mass spectrometry is an identity technique, not a purity technique, and conflating the two is a common source of false confidence.

The baseline noise on a mass spectrum sets the limit of detection, and a weak signal close to the noise is not reliable evidence for the presence of a species.

A mass shift of minus one hundred and twenty-eight usually means a missing Gln or Lys residue from a synthesis deletion sequence.

Worth noting that source contamination is common and silent, so a result that looks too good to be true often is.

The practical summary: use mass spectrometry for identity, not for purity.